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arXiv · 1202.4168

On the two-steps relaxation of mean-field glasses: p-spin model

Ulisse Ferrari·Luca Leuzzi·Giorgio Parisi·Tommaso Rizzo
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Abstract

Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time correlation function at dynamic criticality. In this work we derive critical slowing down exponents of spin-glass models undergoing discontinuous transitions by computing their Gibbs free energy and connecting the dynamic behavior to static "in-state" properties. Both the spherical and Ising versions are considered and, in the simpler spherical case, a generalization to arbitrary schematic Mode Coupling kernels is presented. Comparison with dynamic results available in literature is performed. Analytical predictions for the Ising case are provided for any $p$.

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Ulisse Ferrari, Luca Leuzzi, Giorgio Parisi, Tommaso Rizzo. 2012-02-19. On the two-steps relaxation of mean-field glasses: p-spin model. https://doi.org/10.1103/physrevb.86.014204

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