# LPTMS Publications

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## Alternative solutions to diluted p-spin models and XORSAT problems

### Marc Mézard

^{1}, Federico Ricci-Tersenghi^{2}, Riccardo Zecchina^{3}#### Journal of Statistical Physics

**111**(2003) 505-533We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of the phase diagram: location of the phase transitions (static and dynamic), together with a description of the clustering phenomenon taking place in configurational space. We use two alternative methods: the cavity approach and a rigorous derivation.

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

## Asymptotic behaviour of multiple scattering on infinite number of parallel half-plane

### Bogomolny, E., Schmit, C.

#### Nonlinearity 16 (2003) 2035-2059

Details## Brownian Motion in wedges, last passage time and the second arc-sine law

### Alain Comtet

^{1, 2}, Jean Desbois^{1}#### Journal of Physics A

**36**(2003) L255-L262We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \{OI_i ; i=1,2,..., n\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\arcsin $ or $(\arcsin)^2 $ functions. The original result of Levy is recovered as the special case $n=2$. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed.

- 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 2. IHP, Institut Henri Poincaré

**3**)## Charge and current distribution in graphs

### Christophe Texier

^{1, 2}, Pascal Degiovanni^{3}#### Journal of Physics A

**36**(2003) 12425-12452We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.

- 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
- 3. Laboratoire de Physique de l'ENS Lyon (Phys-ENS), CNRS : UMR5672 – École Normale Supérieure - Lyon

**4**)## Clustering and thermodynamics in the lattice-gas model

### Campi, X., Krivine, H., Krivine, J.

#### Physica A 320 (2003) 41-50

## Dense loops, supersymmetry, and Goldstone phases in two dimensions

### Jesper-Lykke Jacobsen

^{1}, Nicholas Read^{2}, Hubert Saleur^{3}#### Physical Review Letters

**90**(2003) 090601Loop models in two dimensions can be related to O(N) models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for N<2. We argue that this phase is generic for -2< N <2 when crossings of loops are allowed, and distinct from the model of non-crossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].

- 2. Department of Physics, Yale University
- 3. Department of Physics and Astronomy, University of Southern California

**38**)## Dynamique vitreuse de l’espace des phases à l’espace réel

### Bertin, E.

#### . Thèse-CEA Saclay (2003)

## Electron’s selftrapping at the field-effet junction of a molecular crystal

### Kirova, N., Bussac, M.-N.

#### Physical Review B 68 (2003) 235312

## Energy exponents and corrections to scaling in Ising spin glasses

### Jean-Philippe Bouchaud

^{1}, Florent Krzakala^{2, 3}, Olivier C. Martin^{1, 2}#### Physical Review B

**68**(2003) 224404We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

- 1. Service de physique de l'état condensé (SPEC), CNRS : URA2464 – CEA : DSM/IRAMIS
- 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS : UMR8626 – Université Paris XI - Paris Sud
- 3. Dipartimento di Fisica, INFM – SMC – Università degli studi di Roma I - La Sapienza

**65**)## Exercices de mathématiques pour physiciens

### Krivine, H.

#### Ed. Cassini (2003)

## Ferroelectric Mott-Hubbard phase in organic conductors

### Serguei Brazovskii

^{1}, Pierre Monceau^{2}, F. Ya Nad^{3}#### Synthetic Metals

**137**(2003) 1331-1333We present key issues of related phenomenons of the Ferroelectricity and the Charge Disproportionation in organic metals. In (TMTTF_2X the dielectric susceptibility demonstrates clear cases of the ferroelectric and anti-ferroelectric phase transitions. Both the susceptibility and the conductivity prove independence and occasional coexistence of 'structurless' ferroelectric transitions and usual 'anionic' ones. Their sequence gives access to physics of three types of solitons emerging upon cooling via several steps of symmetry breaking. The theory invokes a concept of the Combined Mott-Hubbard State which focuses upon weak processes of electronic Umklapp scattering coming from both the build-in nonequivalence of bonds and the spontaneous one of sites. We propose that the charge ordering in its form of the ferroelectricity exists hiddenly even in the Se subfamily (TMTSF)_2X, giving rise to the unexplained yet low frequency optical peak and the enhanced pseudogap.

- 2. Centre de Recherches sur les Très Basses Températures (CRTBT), CNRS : UPR5001 – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
- 3. Institute of Radioelectronics, Russian Academy of Sciences

## Interlayer tunneling spectroscopy of the charge density wave (CDW) state in NbSe3

### Latyshev, Yu-I., Monceau, P., Sinchenko, A.-A., Bulaevskii, L.-N., Brazovskii, S., Kawae, T., Yamashitz, T.

#### Journal of Physics A: Math. Gen. 36 (2003) 9323

## Large geometric phases and non-elementary monopoles

### Leboeuf, P., Mouchet, A.

#### Journal of Physics A: Math. Gen. 36 (2003) 2847-2856

Details## Local excitations of a spin glass in a magnetic field

### Julien Lamarcq

^{1}, Jean-Philippe Bouchaud^{1}, Olivier C. Martin^{2}#### Physical Review B

**68**(2003) 012404We study the minimum energy clusters (MEC) above the ground state for the 3-d Edwards-Anderson Ising spin glass in a magnetic field. For fields B below 0.4, we find that the field has almost no effect on the excitations that we can probe, of volume V <= 64. As found previously for B=0, their energies decrease with V, and their magnetization remains very small (even slightly negative). For larger fields, both the MEC energy and magnetization grow with V, as expected in a paramagnetic phase. However, all results appear to scale as BV (instead of the B sqrt(V) expected from droplet arguments), suggesting that the spin glass phase is destroyed by any small field. Finally, the geometry of the MEC is completely insensitive to the field, giving further credence that they are lattice animals, in the presence or the absence of a field.

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

**17**)## Local Friedel sum rule on graphs

### Christophe Texier

^{1, 2}, Markus Buttiker^{3}#### Physical Review B

**67**(2003) 245410We consider graphs made of one-dimensional wires connected at vertices and on which may live a scalar potential. We are interested in a scattering situation where the graph is connected to infinite leads. We investigate relations between the scattering matrix and the continuous part of the local density of states, the injectivities, emissivities and partial local density of states. Those latter quantities can be obtained by attaching an extra lead at the point of interest and by investigating the transport in the limit of zero transmission into the additional lead. In addition to the continuous part related to the scattering states, the spectrum of graphs may present a discrete part related to states that remain uncoupled to the external leads. The theory is illustrated with the help of a few simple examples.

- 2. Laboratoire de Physique des Solides (LPS), CNRS : UMR8502 – Université Paris XI - Paris Sud
- 3. Département de Physique Théorique, University of Geneva

**7**)## Loop models from Coulomb gases and supersymmetry: Goldstone phases in two-dimensional polymers. Dans Gazeau J-P. et al (eds), Physical and mathematical aspects of symmetries: proceedings of the 24th international colloquium on group theoretical methods in physics

### Jacobsen, J.L.

#### Institute of Physics Conference Series 173 (2003) 323-326

## Martin Gutzwiller : Un fisic singular (interview)

### Bohigas, O., Navarro, J.

#### Mètode 35 (2003) 72-78

## Matrix models and the enumeration of alternating tangles

### Jacobsen, J.L., Zinn-Justin, P.

#### Markov Processes and Related Fields 9 (2003) 301-310

## Mesoscopic Fluctuations in Quantum Dots in the Kondo Regime

### Ribhu K. Kaul

^{1}, Denis Ullmo^{1, 2}, Harold U. Baranger^{1}#### Physical Review B

**68**(2003) 161305Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime.

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

**6**)## Metastable configurations on the Bethe lattice

### Andrea Pagnani

^{1}, Giorgio Parisi^{2}, Mathieu Ratieville^{1, 2}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**67**(2003) 026116We present a general analytic method to compute the number of metastable configurations as a function of the energy for a system of interacting Ising spins on the Bethe lattice. Our approach is based on the cavity method. We apply it to the case of ferromagnetic interactions, and also to the binary and Gaussian spin glasses. Most of our results are obtained within the replica symmetric ansatz, but we illustrate how replica symmetry breaking can be performed.

- 2. Dipartimento di Fisica, SMC, INFM, and INFN, Università degli studi di Roma I - La Sapienza

**7**)## Near optimal configurations in mean field disordered systems

### Andrea Pagnani

^{1}, Giorgio Parisi^{2}, Mathieu Ratieville^{1, 2}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**68**(2003) 046706We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean field diluted spin glass. As a byproduct of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.

- 2. Dipartimento di Fisica, SMC, INFM, and INFN, Università degli studi di Roma I - La Sapienza

**18**)## On Breaking Time Reversal in a Simple, Smooth, Chaotic System

### Steven Tomsovic

^{1}, Denis Ullmo^{2, 3}, Tatsuro Nagano^{1}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**67**(2003) 067201Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with chaotic classical analogs. For practical reasons, much of the supporting numerical studies of symmetry breaking have been done with billiards or maps, and little with simple, smooth systems. There are two main difficulties in attempting to break time reversal invariance in a continuous time system with a smooth potential. The first is avoiding false symmetry breaking. The second is locating a parameter regime in which the symmetry breaking is strong enough to transition the fluctuation properties fully toward the broken symmetry case, and yet remain weak enough so as not to regularize the dynamics sufficiently that the system is no longer chaotic. We give an example of a system of two-coupled quartic oscillators whose energy level statistics closely match those of the Gaussian unitary ensemble, and which possesses only a minor proportion of regular motion in its phase space.

- 1. Department of Physics, Washington State University
- 3. Duke Physics, Duke University

## On some integrals over the U(N) unitary group and their large N limit

### Paul Zinn-Justin

^{1}, Jean-Bernard Zuber^{2}#### Journal of Physics A

**36**(2003) 3173-3194The integral over the U(N) unitary group $I=\int DU \exp\Tr A U B U^\dagger$ is reexamined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments: relation with integrable Toda lattice hierarchy, diagrammatic expansion and combinatorics, and on what they teach us on the large $N$ limit of $\log I$.

- 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot
- 2. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

**22**)## On the formal equivalence of the TAP and thermodynamic methods in the SK model

### Andrea Cavagna

^{1}, Irene Giardina^{1}, Giorgio Parisi^{1}, Marc Mézard^{2}#### Journal of Physics A

**36**(2003) 1175-1194We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the Becchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general equivalence of TAP and replica partition functions, and show that the annealed calculation of the TAP complexity is formally identical to the quenched thermodynamic calculation of the free energy at one step level of replica symmetry breaking. The complexity we obtain by means of the BRST symmetry turns out to be considerably smaller than the previous non-symmetric value.

- 1. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica, Università degli studi di Roma I - La Sapienza

**28**)## Order-parameter fluctuations in Ising spin glasses at low temperatures

### Matteo Palassini

^{1}, Marta Sales^{2}, Felix Ritort^{3}#### Physical Review B

**68**(2003) 224430We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A and G, show that the order parameter is not self-averaging, consistent with a zero-temperature thermal exponent value \theta' \simeq 0, and confirm the validity of the relation G=1/3 in the thermodynamic limit in the whole low-temperature phase, as predicted by stochastic stability arguments.

- 2. Chemical and Biological Engineering Department, Northwestern University
- 3. Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona

**7**)## Parafermionic theory with the symmetry Z_5

### Dotsenko, Vl.S., Jacobsen, J.L., Santachiara, R.

#### Nuclear Physics B 656 (2003) 259-324

Details## Parafermionic theory with the symmetry Z_N, for N odd

### Dotsenko, Vl.S., Jacobsen, J.L., Santachiara, R.

#### Nuclear Physics B 664 (2003) 477-511

Details## Passing messages between disciplines

### Mezard, M.

#### Sciences 301 (2003) 1686

## Phase transition-like behavior in low-pass filter

### Krivine, H., Lesne, A.

#### American Journal of Physics 71 (2003) 31-33

## Prime Correlations and Fluctuations

### Leboeuf, P.

#### Annales Henri Poincaré 4 (2003) 635-660

## Pseudogaps due to sound modes: from incommensurate charge density waves to semiconducting wires

### Serguei Brasovskii

^{1}, Sergey I. Matveenko^{1, 2}#### JETP Letters

**96**(2003) 555We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes.

- 2. L.D. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics

## Quantum dot ground state energies and spin polarizations: soft versus hard chaos

### Denis Ullmo

^{1, 2}, Tatsuro Nagano^{3}, Steven Tomsovic^{3}#### Physical Review Letters

**90**(2003) 176801We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that ``mesoscopic Stoner fluctuations'', that arise from the residual screened Coulomb interaction, are very sensitive to the degree of chaos. It leads to ground state energies and spin-polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.

- 2. Duke Physics, Duke University
- 3. Department of Physics, Washington State University

**2**)## Quantum thermodynamic fluctuations of a chaotic Fermi-gas model

### Patricio Leboeuf

^{1}, Alejandro Monastra^{2}#### Nuclear Physics A

**724**(2003) 69-84We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully chaotic classical dynamics. The probability distributions of the quantum fluctuations of the grand potential and entropy of the gas are computed as a function of temperature and compared, with good agreement, with general predictions obtained from random matrix theory and periodic orbit theory (based on prime numbers). In each case the universal and non--universal regimes are identified.

- 2. Department of Physics of Complex Systems, Weizmann Institute of Science

**4**)## Random walks on three-strand braids and on related hyperbolic groups

### Nechaev, S., Voituriez, R.

#### Journal of Physics A: Math. Gen. 36 (2003) 43-66

## Repliement d’hétéropolymères

### MÃ_ller, M.

#### . Thèse-LPTMS Orsay (2003)

## Scaling of domain wall energies in two dimensional Ising spin glasses

### Amoruso, C., Marinari, E., Martin, O.C., Pagnani, A.

#### Physical Review Letters 91 (2003) 087201

Details## Solitonic transmission of Böse-Einstein matter waves

### Leboeuf, P., Pavloff, N., Sinha, S.

#### Physical Review A 68 (2003) 063608

Details## Some detailed mean field predictions for disordered systems

### Rattieville, M.

#### . Thèse-LPTMS Orsay (2003)

## Spectral properties of distance matrices

### Eugène Bogomolny

^{1}, Oriol Bohigas^{1}, Charles Schmit^{1}#### Journal of Physics A

**36**(2003) 3595-3616Distance matrices are matrices whose elements are the relative distances between points located on a certain manifold. In all cases considered here all their eigenvalues except one are non-positive. When the points are uncorrelated and randomly distributed we investigate the average density of their eigenvalues and the structure of their eigenfunctions. The spectrum exhibits delocalized and strongly localized states which possess different power-law average behaviour. The exponents depend only on the dimensionality of the manifold.

**7**)## Statistical Physics of RNA-folding

### Markus Muller

^{1}#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

**67**(2003) 021914We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large enough costs the model exhibits a thermal denaturation transition which we analyze in terms of the radius of gyration. We point out an inconsistency in the standard approach to RNA secondary structure prediction for large molecules. Under an external force a second order phase transition between a globular and an extended phase takes place. A Harris-type criterion shows that sequence disorder does not affect the correlation length exponent while the other critical exponents are modified in the glass phase. However, at high temperatures, on a coarse-grained level, disordered RNA is well described by a homogeneous model. The characteristics of force-extension curves are discussed as a function of the energy parameters. We show that the force transition is always second order. A re-entrance phenomenon relevant for real disordered RNA is predicted.

**27**)## Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses

### Munetaka Sasaki

^{1}, Olivier C. Martin^{2}#### Physical Review Letters

**91**(2003) 097201We use simulations within the Migdal-Kadanoff real space renormalization approach to probe the scales relevant for rejuvenation and memory in spin glasses. One of the central questions concerns the role of temperature chaos. First we investigate scaling laws of equilibrium temperature chaos, finding super-exponential decay of correlations but no chaos for the total free energy. Then we perform out of equilibrium simulations that follow experimental protocols. We find that: (1) rejuvenation arises at a length scale smaller than the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes out to length scales much larger than l(T,T').

- 1. Institute for Solid State Physics (ISSP), University of Tokyo

**16**)## The asymmetric ABAB matrix model

### Paul Zinn-Justin

^{1}#### Europhysics Letters (EPL)

**64**(2003) 737-742In this letter, it is pointed out that the two matrix model defined by the action S=(1/2)(tr A^2+tr B^2)-(alpha_A/4) tr A^4-(alpha_B/4) tr B^4-(beta/2) tr(AB)^2 can be solved in the large N limit using a generalization of the solution of Kazakov and Zinn-Justin (who considered the symmetric case alpha_A=alpha_B). This model could have useful applications to 3D Lorentzian gravity.

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

**6**)## The cavity method at zero temperature

### Marc Mézard

^{1}, Giorgio Parisi^{2}#### Journal of Statistical Physics

**111**(2003) 1-34In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a Bethe lattice. The computation is done explicitly in the formalism equivalent to 'one step replica symmetry breaking'; we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three.

- 2. Dipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM, Università degli studi di Roma I - La Sapienza

## The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

### Paul Zinn-Justin

^{1}#### Communications in Mathematical Physics

**238**(2003) 287-304The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.

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

**6**)## The Impact of Discoveries of Ferroelectricity and Charge Disproportionation in Organic Conductors

### Serguei Brazovskii

^{1}#### Synthetic Metals

**133-134**(2003) 301-303Discoveries of the Ferroelectric anomaly (Nad, Monceau, et al) and of the related charge disproportionation (Brown et al) call for a revaluation of the phase diagram of the (TMTTF)2X compounds and return the attention to the interplay of electronic and structural properties. We shall describe a concept of the Combined Mott-Hubbard state as the source for the ferroelectricity. We shall demonstrate the existence of two types of spinless solitons: pi- solitons, the holons, are observed via the activated conductivity; the noninteger alpha- solitons are responsible for the depolarization of the FE order. We propose that the (anti) ferroelectricity does exists hiddenly even in the Se subfamily, giving rise to the unexplained yet optical peak. We remind then the abandoned theory by the author and Yakovenko for the universal phase diagram which we contrast with the recent one.

## The LLL Anyon equation of state in the antiscreening regime

### Stefan Mashkevich

^{1}, Stéphane Ouvry^{2}#### Physics Letters A

**310**(2003) 85-94The thermodynamics of the anyon model projected on the lowest Landau level (LLL) of an external magnetic field is addressed in the anti-screening regime, where the flux tubes carried by the anyons are parallel to the magnetic field. It is claimed that the LLL-anyon equation of state, which is known in the screening regime, can be analytically continued in the statistical parameter across the Fermi point to the antiscreening regime up to the vicinity (whose width tends to zero when the magnetic field becomes infinite) of the Bose point. There, an unphysical discontinuity arises due to the dropping of the non-LLL eigenstates which join the LLL, making the LLL approximation no longer valid. However, taking into account the effect of the non-LLL states at the Bose point would only smoothen the discontinuity and not alter the physics which is captured by the LLL projection: Close to the Bose point, the critical filling factor either goes to infinity (usual bosons) in the screening situation, or to 1/2 in the anti-screening situation, the difference between the flux tubes orientation being relevant even when they carry an infinitesimal fraction of the flux quantum. An exclusion statistics interpretation is adduced, which explains this situation in semiclassical terms. It is further shown how the exact solutions of the 3-anyon problem support this scenario as far as the third cluster coefficient is concerned.

- 1. Bogolyubov Institute for Theoretical Physics, Bogolyubov Institute for Theoretical Physics

**1**)## Topological character of excitations in strongly correlated electronic systems: confinement and dimensional crossover

### Brazovskii, S., Kirova, N.

#### Synthetic Metals 133 (2003) 41

## Topological correlations in trivial knots: new arguments in support of the crumpled polymer globule

### Oleg A. Vasilyev

^{1}, Sergei K. Nechaev^{1, 2}#### Theoretical and Mathematical Physics

**134**(2003) 142-159We prove the fractal crumpled structure of collapsed unknotted polymer ring. In this state the polymer chain forms a system of densely packed folds, mutually separated in all scales. The proof is based on the numerical and analytical investigation of topological correlations in randomly generated dense knots on strips $L_{v} \times L_{h}$ of widths $L_{v}=3,5$. We have analyzed the conditional probability of the fact that a part of an unknotted chain is also almost unknotted. The complexity of dense knots and quasi--knots is characterized by the power $n$ of the Jones--Kauffman polynomial invariant. It is shown, that for long strips $L_{h} \gg L_{v}$ the knot complexity $n$ is proportional to the length of the strip $L_{h}$. At the same time, the typical complexity of the quasi--knot which is a part of trivial knot behaves as $n\sim \sqrt{L_{h}}$ and hence is significantly smaller. Obtained results show that topological state of any part of the trivial knot in a collapsed phase is almost trivial.

- 1. L.D.Landau Institute for Theoretical Physics, Russian Academy of Sciences

## Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial

### Jesper-Lykke Jacobsen

^{1}, Jesus Salas^{2}, Alan D. Sokal^{3}#### Journal of Statistical Physics

**112**(2003) 921-1017We study the chromatic polynomial P_G(q) for m \times n triangular-lattice strips of widths m <= 12_P, 9_F (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin--Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m,n\to\infty and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

- 2. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza
- 3. Department of Physics, New York University

## Unified theory for optics of conducting polymers

### Kirova, N., Brazovskii, S.

#### Synthetic Metals 135 (2003) 461

## XY frustrated systems: Continuous exponents in discontinuous phase transitions

### Mathieu Tissier

^{1}, Bertrand Delamotte^{2}, Dominique Mouhanna^{2}#### Physical Review B

**67**(2003) 134422XY frustrated magnets exhibit an unsual critical behavior: they display scaling laws accompanied by nonuniversal critical exponents and a negative anomalous dimension. This suggests that they undergo weak first order phase transitions. We show that all perturbative approaches that have been used to investigate XY frustrated magnets fail to reproduce these features. Using a nonperturbative approach based on the concept of effective average action, we are able to account for this nonuniversal scaling and to describe qualitatively and, to some extent, quantitatively the physics of these systems.

- 2. 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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