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Quantitative field theory of the glass transition

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arxiv 1206.2482 v3 pith:YDRNP437 submitted 2012-06-12 cond-mat.dis-nn cond-mat.stat-mech

Silvio Franz , Hugo Jacquin , Giorgio Parisi , Pierfrancesco Urbani , Francesco Zamponi This is my paper · ORCID
classification cond-mat.dis-nncond-mat.stat-mech
keywords criticaldynamicalfieldtheoryanalysiscorrelationobtainresults
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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.

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