Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 109, Issue 46, Pages 18725-18730Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1216578109
Keywords
mode-coupling theory; perturbative expansion; replica theory
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Funding
- Foundation Fondation Capital Fund Management-Jean Pierre Aguilar grant
- European Research Council [247328]
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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 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.
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