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

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 $p$.

9 pages

References in corpus (5)

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Cited by in corpus (4)

• Critical Dynamics in Glassy Systems
• Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach
• Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models
• A note on weakly discontinuous dynamical transitions