Quantitative field theory of the glass transition

Abstract

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.

6 pages, 2 figures + supplementary information -- a few minor errors of the published version have been fixed

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• Liu-Nagel phase diagrams in infinite dimension
• Qualitative Features at the Glass Crossover
• Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
• Marginally stable phases in mean-field structural glasses
• Statistical mechanics models for multimode lasers and random lasers
• Long-range spatial correlations of particle displacements and the emergence of elasticity
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• Finite-dimensional vestige of spinodal criticality above the dynamical glass transition
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• Critical dynamical heterogeneities close to continuous second-order glass transitions
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
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• Solving Optimization Problems by the Public Goods Game
• Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach
• A self-consistent field theory of density correlations in classical fluids
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• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids
• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain