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.

Quantitative field theory of the glass transition / Franz, S.; Jacquin, H.; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, F.. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - 109:46(2012), pp. 18725-18730. [10.1073/pnas.1216578109]

Quantitative field theory of the glass transition

PARISI, Giorgio;URBANI, PIERFRANCESCO;F. Zamponi
2012

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.
2012
mode-coupling theory; perturbative expansion; replica theory
01 Pubblicazione su rivista::01a Articolo in rivista
Quantitative field theory of the glass transition / Franz, S.; Jacquin, H.; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, F.. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - 109:46(2012), pp. 18725-18730. [10.1073/pnas.1216578109]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/510221
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