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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 analytically study 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 for the Gibbs free energy, and we find results that are consistent with numerical simulations.

SUBMITTER: Franz S 

PROVIDER: S-EPMC3503232 | biostudies-other | 2012 Nov

REPOSITORIES: biostudies-other

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Quantitative field theory of the glass transition.

Franz Silvio S   Jacquin Hugo H   Parisi Giorgio G   Urbani Pierfrancesco P   Zamponi Francesco F  

Proceedings of the National Academy of Sciences of the United States of America 20121029 46

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 analytically study 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  ...[more]

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