Quantitative field theory of the glass transition

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

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 MSC - Matière et Systèmes Complexes
3 Dipartimento di Fisica and INFM
4 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Silvio Franz, Hugo Jacquin, Giorgio Parisi, Pierfrancesco Urbani, Francesco Zamponi. Quantitative field theory of the glass transition. Proceedings of the National Academy of Sciences of the United States of America, 2012, 109 (46), pp.18725-18730. ⟨10.1073/pnas.1216578109⟩. ⟨hal-00795210⟩