LPTMS Publications

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• A ferromagnet with a glass transition

Silvio Franz 1, Marc Mézard 2, Federico Ricci-Tersenghi 1, Martin Weigt 3, Riccardo Zecchina 1

Europhysics Letters (EPL) 55 (2001) 465

We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one step replica-symmetry broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level.

• 1. International Centre for Theoretical Physics (ICTP), the Abdus Salam International Centre for Theoretical Physics
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Institute for Theoretical Physics, University of Göttingen

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• A hierarchical approach for computing spin glass ground states

Jérôme Houdayer 1, Olivier C. Martin 2

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 64 (2001) 056704

We describe a numerical algorithm for computing spin glass ground states with a high level of reliability. The method uses a population based search and applies optimization on multiple scales. Benchmarks are given leading to estimates of the performance on large lattices.

• 1. Institut für Physik/Max Planck Institut für Polymerforschung, Max-Planck-Institut
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• A transfer matrix approach to the enumeration of colored links Authors: Jesper Jacobsen,

Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

Journal of Knot Theory and Its Ramifications 10 (2001) 1233-1267

We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight $n$ to each connected component. Considering more general tetravalent diagrams with self-intersections and tangencies allows us to treat topological (flype) equivalences. This is done by means of a finite renormalization scheme for an associated matrix model. We give results, expressed as polynomials in $n$, for the various generating functions up to order 19 (link diagrams), 15 (prime alternating tangles) and 11 (6-legged links) intersections. The limit $n\to\infty$ is solved explicitly. We then analyze the large-order asymptotics of the generating functions. For $0\le n \le 2$ good agreement is found with a conjecture for the critical exponent, based on the KPZ relation.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences

Alexei A. Naidenov 1, Sergei K. Nechaev 1, 2

Journal of Physics A 34 (2001) 5625-5634

The adsorption of an ideal heteropolymer loop at a potential point well is investigated within the frameworks of a standard random matrix theory. On the basis of semi-analytical/semi-numerical approach the histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain's links is constructed. It is shown that the sequences having the transition points in the tail of the histogram display the correlations between nearest-neighbor monomers.

• 1. L D Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Bose beams: coherent propagation through a guide

Patricio Leboeuf 1, Nicolas Pavloff 1

Physical Review A: Atomic, Molecular and Optical Physics 64 (2001) 033602

We compute the stationary profiles of a coherent beam of Bose condensed atoms propagating through a guide. Special emphasis is put on the effect of an obstacle present on the trajectory of the beam. The obstacle considered (such as a bend in the guide, or a laser field perpendicular to the beam) results in a repulsive or an attractive potential acting on the condensate. Different behaviors are observed when varying the beam velocity (with respect to the speed of sound), the size of the obstacle (relative to the healing length) and the intensity and sign of the potential. The existence of bound states of the condensate is also considered.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Classification of Conformal Field Theories Based on Coulomb gases. Application to Loop Models

Vladimir S. Dotsenko 1, Jesper Lykke Jacobsen 2, Marco Picco 1

Nuclear Physics B 618 (2001) 523

We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Discrete energy landscapes and replica symmetry breaking at zero temperature

Florent Krzakala 1, Olivier C. Martin 1

Europhysics Letters (EPL) 53 (2001) 749-755

The order parameter P(q) for disordered systems with degenerate ground-states is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at zero temperature as in the non-degenerate case, even if there are zero-energy large-scale excitations (complex energy landscape). Such a situation should arise in the 3-dimensional +-J Ising spin glass and in MAX-SAT. Also, we argue that if the energy landscape is complex with a finite number of ground-state families, then replica symmetry breaking reappears at positive temperature.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Discrete thermodynamic Bethe ansatz

Michel Bergere 1, Ken-Ichiro Imura 2, Stéphane Ouvry 2

Nuclear Physics B 608 (2001) 577

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero-Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero-Moser thermodynamics. We apply this algorithm to the Lieb-Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose-Einstein condensates in one dimension. We find that the discrete TBA reproduces correctly the N-body groundstate energy of the Lieb-Liniger model in a harmonic well at first order in perturbation theory, but corrections do appear at second order.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Equilibrium valleys in spin glasses at low temperature

Enzo Marinari 1, Olivier C. Martin 2, Francesco Zuliani 2

Physical Review B 64 (2001) 184413

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.

• 1. Dipartimento di Fisica, INFM and INFN, Università degli studi di Roma I - La Sapienza
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

O. Benichou 1, 2, A. M. Cazabat 3, J. De Coninck, M. Moreau 2, G. Oshanin 2

Physical Review B 63 (2001) 235413

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique Théorique des Liquides (LPTL), CNRS : UMR7600 – Université Paris VI - Pierre et Marie Curie
• 3. Laboratoire de Physique de la Matière Condensée (LPMC), CNRS : UMR7125 – Collège de France

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• Friedel Oscillations and Charge-density Waves Pinning in Quasi-one-dimensional Conductors: An X-ray Access

Sylvain Ravy 1, Stephan Rouzière 2, Jean-Paul Pouget 1, Serguei Brazovskii 3

Synthetic Metals 120 (2001) 1075

We present an x-ray diffraction study of the Vanadium-doped blue bronze K0.3(Mo0.972V0.028)O3. At low temperature, we have observed both an intensity asymmetry of the +-2kF satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that the profile asymmetry is due to Friedel oscillation around the V substituant and that the intensity asymmetry is related to the charge density wave (CDW) pinning. These two effects, intensity and profile asymmetries, gives for the first time access to the local properties of CDW in disordered systems, including the pinning and even the phase shift of FOs.

• 1. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
• 2. School of Chemistry, Physics and Environmental Science, University of Sussex
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings

Denis Ullmo 1, Harold U. Baranger 2

Physical Review B 64 (2001) 245324

We use random matrix models to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions treated in Hartree-Fock. This model is applicable to chaotic quantum dots or nanoparticles--in these systems the single-particle statistics follows random matrix theory at energy scales less than the Thouless energy. We find the distribution of Coulomb blockade peak spacings first for a large dot in which the residual interactions can be taken constant: the spacing fluctuations are of order the mean level separation Delta. Corrections to this limit are studied using the small parameter 1/(kf L): both the residual interactions and the effect of the changing confinement on the single-particle levels produce fluctuations of order Delta/sqrt(kf L). The distributions we find are significantly more like the experimental results than the simple constant interaction model.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Duke Physics, Duke University

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• Marginal pinning of vortices at high temperature

Markus Muller 1, 2, Denis A. Gorokhov 1, 3, Gianni Blatter 1

Physical Review B 64 (2001) 134523

We analyze the competition between thermal fluctuations and pinning of vortices in bulk type II superconductors subject to point-like disorder and derive an expression for the temperature dependence of the pinning length L_c(T) which separates different types of single vortex wandering. Given a disorder potential with a basic scale \xi and a correlator K_0(u) \sim K_0 (u/xi)^{-\beta} ln^alpha (u/xi) we determine the dependence of L_c(T) on the correlator range: correlators with \beta > 2 (short-range) and \beta <2 (long-range) lead to the known results L_c(T) \sim L_c(0) exp[C T^3] and L_c(T) \sim L_c(0) (C T)^{(4+beta)/(2-beta)}, respectively. Using functional renormalization group we show that for \beta =2 the result takes the interpolating form L_c(T) \sim L_c(0) exp[C T^{3/(2+alpha)}]. Pinning of vortices in bulk type II superconductors involves a long-range correlator with \beta=2, \alpha=1 on intermediate scales \xi

• 1. Theoretische Physik, ETH-Hönggerberg, ETH-Hönggerberg
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Department of Physics, University of Harvard

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• Microscopic Models for Long Ranged Volatility Correlations

Irene Giardina 1, Jean-Philippe Bouchaud 2, 3, Marc Mézard 4

Physica A 299 (2001) 28-39

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between active' and inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy, or a more sophisticated version that includes some price dynamics. We show that real market data can be surprisingly well accounted for by these simple models.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 3. Science & Finance, Sciences et Finances
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Multifractality in uniform hyperbolic lattices and in quasi-classical Liouville field theory

Alain Comtet 1, Sergei K. Nechaev 1, Raphael Voituriez 1

Journal of Statistical Physics 102 (2001) 203-230

We introduce a deterministic model defined on a two dimensional hyperbolic lattice. This model provides an example of a non random system whose multifractal behaviour has a number theoretic origin. We determine the multifractal exponents, discuss the termination of multifractality and conjecture the geometric origin of the multifractal behavior in Liouville quasi--classical field theory.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• On a universal mechanism for long ranged volatility correlations

Jean-Philippe Bouchaud 1, 2, Irene Giardina 3, Marc Mézard 4

Quantitative Finance 1 (2001) 212-216

We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between active' and inactive' strategies is subordinated to random-walk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be surprisingly well accounted for by these simple models.

• 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 2. Science & Finance, Science et Finances
• 3. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 4. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• On the Plants Leaves Boundary, ‘Jupe à Godets’ and Conformal Embeddings

Sergei K. Nechaev 1, 2, Raphael Voituriez 1

Journal of Physics A 34 (2001) 11069-11082

he stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a 'surface à godets'. It is shown that the information on the profile is encoded in the Jacobian of a conformal mapping (the coefficient of deformation) corresponding to an isometric embedding of a uniform Cayley tree into the 3D Euclidean space. The geometric characteristics of the leaf's boundary (like the perimeter and the height) are calculated. In addition a symbolic language allowing to investigate statistical properties of a 'surface à godets' with annealed random defects of curvature of density $q$ is developed. It is found that at $q=1$ the surface exhibits a phase transition with critical exponent $\alpha=1/2$ from the exponentially growing to the flat structure.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. L D Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• On the Relation between the anyon and the Calogero Models

Stéphane Ouvry 1

Physics Letters B 510 (2001) 335

In order to achieve a dimensional reduction from dimension two to one not only in phase space but also in configuration space, the lowest Landau level (LLL) projection is not sufficient. One has also, in the LLL, to take the vanishing magnetic field limit, a procedure which can be given a non ambiguous meaning by means of a long distance regulator. As an illustration, the equivalence of the LLL anyon model in the vanishing magnetic field limit to the Calogero model is established. A thermodynamical argument is proposed which supports this claim. Some general considerations in favor of an intimate connexion between anyon and Haldane statistics are also given.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Percolation line of stable clusters in supercritical fluids

Xavier Campi 1, Hubert Krivine 1, Nicolas Sator 1

Physica A 296 (2001) 24-30

We predict that self-bound clusters of particles exist in the supercritical phase of simple fluids. These clusters, whose internal temperature is lower than the global temperature of the system, define a percolation line that starts at the critical point. This line should be physically observable. Possible experiments showing the validity of these predictions are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Periodic orbits contribution to the 2-point correlation form factor for pseudo-integrable systems

Eugene Bogomolny 1, Olivier Giraud 1, Charles Schmit 1

Communications in Mathematical Physics 222 (2001) 327-369

The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal approximation. The following cases are considered: (i) plane billiards in the form of right triangles with one angle $\pi/n$ and (ii) rectangular billiards with the Aharonov-Bohm flux line. In the first model, using the properties of the Veech structure, it is shown that $K_2(0)=(n+\epsilon(n))/(3(n-2))$ where $\epsilon(n)=0$ for odd $n$, $\epsilon(n)=2$ for even $n$ not divisible by 3, and $\epsilon(n)=6$ for even $n$ divisible by 3. For completeness we also recall informally the main features of the Veech construction. In the second model the answer depends on arithmetical properties of ratios of flux line coordinates to the corresponding sides of the rectangle. When these ratios are non-commensurable irrational numbers, $K_2(0)=1-3\bar{\alpha}+4\bar{\alpha}^2$ where $\bar{\alpha}$ is the fractional part of the flux through the rectangle when $0\le \bar{\alpha}\le 1/2$ and it is symmetric with respect to the line $\bar{\alpha}=1/2$ when $1/2 \le \bar{\alpha}\le 1$. The comparison of these results with numerical calculations of the form factor is discussed in detail. The above values of $K_2(0)$ differ from all known examples of spectral statistics, thus confirming analytically the peculiarities of statistical properties of the energy levels in pseudo-integrable systems.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Population dynamics in a random environment

Irene Giardina 1, Jean-Philippe Bouchaud 2, Marc Mézard 3

Journal of Physics A 34 (2001) L245-L252

We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour appears. We introduce the idea of proliferation assisted barrier crossing and give a Flory like argument to understand qualitatively this non trivial diffusive behaviour. A one loop RG analysis close to the critical dimension d_c=2 confirms that the random force fixed point is unstable and flows towards an uncontrolled strong coupling regime.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT
• 2. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Resonance-assisted tunneling in near-integrable systems

Olivier Brodier 1, Peter Schlagheck 1, Denis Ullmo 1

Physical Review Letters 87 (2001) 064101

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasi-degenerate eigenvalues from the purely exponential decrease with 1 / hbar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the KAM tori, allows to quantitatively reproduce the behavior of the eigenvalue splittings.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Scattering theory on graphs

Christophe Texier 1, 2, Gilles Montambaux 2

Journal of Physics A 34 (2001) 10307-10326

We consider the scattering theory for the Schrödinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud

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• Semiclassical Density Functional Theory: Strutinsky Energy Corrections in Quantum Dots

Denis Ullmo 1, Tatsuro Nagano 2, Steven Tomsovic 2, Harold U. Baranger 3

Physical Review B 63 (2001) 125339-1-13

We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these oscillations remain puzzling, however, particularly the statistics of spacings between conductance peaks. To explore the role that residual interactions may play in the spacing statistics, we consider many-body systems which include electron-electron interactions through an explicit density functional. First, we develop an approximate series expansion for obtaining the ground state using the idea of the Strutinsky shell correction method. Next, we relate the second-order semiclassical corrections to the screened Coulomb potential. Finally, we investigate the validity of the approximation method by numerical calculation of a one-dimensional model system, and show the relative magnitudes of the successive terms as a function of particle number.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Department of Physics, Washington State University
• 3. Duke Physics, Duke University

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• Short-range plasma model for intermediate spectral statistics

Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1

European Physical Journal B 19 (2001) 121-132

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number $k$ of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the asymptotic form $\Sigma^2(L)\sim\chi L$ for large $L$ and the nearest-neighbor distribution decreases exponentially when $s\to \infty$, $P(s)\sim\exp (-\Lambda s)$ with $\Lambda=1/\chi=k\beta+1$, where $\beta$ is the inverse temperature of the gas ($\beta=$1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). In the simplest case of $k=\beta=1$, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions e.g. $P(s)=4s\exp(-2s)$. Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare them to the Semi-Poisson statistics.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Physics Department, University of California, San Diego

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• Singular statistics

Eugene Bogomolny 1, Ulrich Gerland 2, Charles Schmit 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 63 (2001) 036206

We consider the statistical distribution of zeros of random meromorphic functions whose poles are independent random variables. It is demonstrated that correlation functions of these zeros can be computed analytically and explicit calculations are performed for the 2-point correlation function. This problem naturally appears in e.g. rank-one perturbation of an integrable Hamiltonian and, in particular, when a $\delta$-function potential is added to an integrable billiard.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Physics Department, University of California, San Diego

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• Some Matrix Integrals related to Knots and Links

Paul Zinn-Justin 1

MSRI Publications 40 (2001) 1

The study of a certain class of matrix integrals can be motivated by their interpretation as counting objects of knot theory such as alternating prime links, tangles or knots. The simplest such model is studied in detail and allows to rederive recent results of Sundberg and Thistlethwaite. The second non-trivial example turns out to be essentially the so-called ABAB model, though in this case the analysis has not yet been carried out completely. Further generalizations are discussed. This is a review of work done (in part) in collaboration with J.-B. Zuber.

• 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot

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• Spectral determinant on graphs with generalized boundary conditions

Jean Desbois 1

European Physical Journal B 24 (2001) 261-266

The spectral determinant of the Schrödinger operator ($- \Delta + V(x)$) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Spectral spacing correlations for chaotic and disordered systems

Oriol Bohigas 1, Patricio Leboeuf 1, Juan Mayor Sanchez 2

Foundations of Physics 31 (2001) 489-517

ew aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron-Frobenius operator, is derived. It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing data''. The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Departamento de Física J. J. Giambiagi, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires

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• Star graphs and Seba billiards

Gregory Berkolaiko 1, Eugene Bogomolny 2, J.P. Keating 3, 4

Journal of Physics A 34 (2001) 335-350

We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. Reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor - the Fourier transform of the two-point correlation function - previously calculated using periodic orbit theory.

• 1. Department of Physics of Complex Systems, Weizmann Institute of Science
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. School of Mathematics, University of Bristol
• 4. Basic Research Institute in Mathematical Sciences (BRIMS), Hewlett-Packard Labs

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• Statistical mechanics methods and phase transitions in optimization problems

Olivier C. Martin 1, Rémi Monasson 2, Riccardo Zecchina 3

Theoretical Computer Science 265 (2001) 3-67

Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer science and statistical physics. This review aims at presenting the tools and concepts designed by physicists to deal with optimization or decision problems in an accessible language for computer scientists and mathematicians, with no prerequisites in physics. We first introduce some elementary methods of statistical mechanics and then progressively cover the tools appropriate for disordered systems. In each case, we apply these methods to study the phase transitions or the statistical properties of the optimal solutions in various combinatorial problems. We cover in detail the Random Graph, the Satisfiability, and the Traveling Salesman problems. References to the physics literature on optimization are provided. We also give our perspective regarding the interdisciplinary contribution of physics to computer science.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. The James Franck Institute, University of Chicago
• 3. International Centre for Theoretical Physics (ICTP), International Centre for Theoretical Physics

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• Statistics of charged solitons and formation of stripes

Sofian Teber 1, Branko P. Stojkovic 2, Serguei Brazovskii 1, A. R. Bishop 2

Journal of Physics: Condensed Matter 13 (2001) 4015-4031

The 2-fold degeneracy of the ground state of a quasi-one-dimensional system allows it to support topological excitations such as solitons. We study the combined effects of Coulomb interactions and confinement due to interchain coupling on the statistics of such defects. We concentrate on a 2D case which may correspond to monolayers of polyacetylene or other charge density waves. The theory is developped by a mapping to the 2D Ising model with long-range 4-spin interactions. The phase diagram exhibits deconfined phases for liquids and Wigner crystals of kinks and confined ones for bikinks. Also we find aggregated phases with either infinite domain walls of kinks or finite rods of bikinks. Roughening effects due to both temperature and Coulomb repulsion are observed. Applications may concern the melting of stripes in doped correlated materials.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory

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• The Bethe lattice spin glass revisited

Marc Mézard 1, Giorgio Parisi 2

European Physical Journal B 20 (2001) 217-240

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Dipartimento di Fisica, Sezione INFN and Unità INFM, Università degli studi di Roma I - La Sapienza

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• The dynamical structure factor in topologically disordered systems

Victor Martin-Mayor 1, Marc Mézard 2, Giorgio Parisi 3, Paolo Verrocchio 4

Journal of Chemical Physics 114 (2001) 8068-8081

A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to that class of systems. The computation describes their relevant spectral features in the region of the high frequency sound. The analytical results are tested with numerical simulations and are found to be in very good agreement with them. Our results may explain the findings of inelastic X-ray scattering experiments in various glassy systems.

• 1. Dipartimento di Fisica, Università degli studi di Roma I - La Sapienza
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. Dipartimento di Fisica, Sezione INFN and Unità INFM, Università degli studi di Roma I - La Sapienza
• 4. Dipartimento di Fisica, Universita di Trento

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• The ferroelectric Mott-Hubbard phase of organic (TMTTF)2X conductors

Pierre Monceau 1, F. Ya Nad 1, 2, Serguei Brazovskii 3, 4

Physical Review Letters 86 (2001) 4080-4083

We present experimental evidences for a ferro-electric transition in the family of quasi one- dimensional conductors (TMTTF)2X. We interpret this new transition in the frame of the combined Mott-Hubbard state taking into account the double action of the spontaneous charge disproportionation on the TMTTF molecular stacks and of the X anionic potentials.

• 1. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2. Institute of Radio-Engineering and Electronics, Institute of Radio-Engineering and Electronics
• 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 4. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

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• The Riemannium

Patricio Leboeuf 1, Alejandro Monastra 1, Oriol Bohigas 1

Regular and Chaotic Dynamics 6 (2001) 205-210

The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up to a Fermi energy $E_F$. The distribution of the total energy is shown to be non-Gaussian, asymmetric, and independent of $E_F$ in the limit $E_F\to\infty$. The moments of the limit distribution are computed analytically. The autocorrelation function, the finite energy corrections, and a comparison with random matrix theory are also discussed.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

Sergei K. Nechaev 1, 2, Oleg A. Vasilyev 2

JETP Letters 93 (2001) 1119-1136

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Landau Institute for Theoretical Physics (ITP), Landau Institute for Theoretical Physics

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• Topological Confinement of Spins and Charges: Spinons as pi-junctions

Serguei Brazovskii 1

EDP Sciences 1 (2001) 315

Topologically nontrivial states, the solitons, emerge as elementary excitations in 1D electronic systems. In a quasi 1D material the topological requirements originate the spin- or charge- roton like excitations with charge- or spin- kinks localized in the core. They result from the spin-charge recombination due to confinement and the combined symmetry. The rotons possess semi-integer winding numbers which may be relevant to configurations discussed in connection to quantum computing schemes. Practically important is the case of the spinon functioning as the single electronic pi- junction in a quasi 1D superconducting material.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Topological relaxation of entangled flux lattices: Single vs collective line dynamics

Ruslan Bikbov 1, Sergei K. Nechaev 1, 2

Physical Review Letters 87 (2001) 150602

A symbolic language allowing to solve statistical problems for the systems with nonabelian braid-like topology in 2+1 dimensions is developed. The approach is based on the similarity between growing braid and 'heap of colored pieces'. As an application, the problem of a vortex glass transition in high-T_c superconductors is re-examined on microscopic level

• 1. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models II. Extended Results for Square-Lattice Chromatic Polynomial

Jesper-Lykke Jacobsen 1, Jesus Salas 2

Journal of Statistical Physics 104 (2001) 701-723

We study the chromatic polynomials for m \times n square-lattice strips, of width 9 <= m <= 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n \to \infty. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza

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• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice

John Cardy 1, Jesper-Lykke Jacobsen 2, Alan D. Sokal 3

Journal of Statistical Physics 105 (2001) 25-47

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as \beta \equiv J/kT \to \infty according to \xi \sim A e^{2\beta} (1 + b\beta e^{-\beta} + ...), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

• 1. Oxford University (THEORETICAL PHYSICS), University of Oxford
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 3. New York University (DEPARTMENT OF PHYSICS), New York University

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• X-Ray Scattering Evidence for Macroscopic Strong Pinning Centers in the Sliding CDW state of NbSe_3

D. Rideau 1, 2, Pierre Monceau 1, Roland Currat 2, Herwig Requardt 3, 4, F. Ya Nad 1, 5, J. Lorenzo 2, 4, Serguei Brazovskii 6, C. Detlefs 4, G. Gruebel 4

Europhysics Letters (EPL) 56 (2001) 289-295

Using high-resolution X-ray scattering techniques, we measure the variation, q(x), of the position in reciprocal space of the CDW satellite, in the sliding state, along the length of NbSe_3 whiskers. We show that structural defects and intentionally X-ray radiation-damaged regions increase locally the CDW pinning force, and induce CDW phase distortions which are consistent with those observed near contacts. Using the semi-microscopic model from Brazovskii describing the normal-condensed carrier conversion, with spatially varying parameters, we account for the experimental spatial dependence of the CDW phase gradient near both types of defects.

• 1. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
• 2. Institut Laue-Langevin, Institut Laue-Langevin
• 3. MPI für Metallforschung, MPI für Metallforschung
• 4. European Synchrotron Radiation Facility (ESRF), ESRF
• 5. Institute of Radio-Engineering and Electronics, Institute of Radio-Engineering and Electronics
• 6. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud

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• Zero-temperature responses of a 3D spin glass in a magnetic field

Florent Krzakala 1, Jérôme Houdayer 2, Enzo Marinari 3, Olivier C. Martin 1, Giorgio Parisi 3

Physical Review Letters 87 (2001) 197204

We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
• 2. Institut für Physik, and Max Planck Institut für Polymerforschung, Max-Planck-Institut
• 3. Dipartimento di Fisica, INFM, SMC, and INFN, Università degli studi di Roma I - La Sapienza