Static replica approach to critical correlations in glassy systems

Silvio Franz 1, Hugo Jacquin 2, Giorgio Parisi 3, Pierfrancesco Urbani 1, Francesco Zamponi 4

Journal of Chemical Physics 138 (2013) 12A540

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.

  • 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2 : Matière et Systèmes Complexes (MSC)
    CNRS : UMR7057 – Université Paris VII - Paris Diderot
  • 3 : Dipartimento di Fisica and INFM
    Università degli studi di Roma I - La Sapienza
  • 4 : Laboratoire de Physique Théorique de l'ENS (LPTENS)
    CNRS : UMR8549 – Université Pierre et Marie Curie (UPMC) - Paris VI – École normale supérieure [ENS] - Paris