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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.