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 $p$.

arXiv comment9 pages

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Cited by in corpus (19)

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• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Optical computation of a spin glass dynamics with tunable complexity
• Diluted Mean-Field Spin-Glass Models at Criticality
• Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems
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• Sampling from Mean-Field Gibbs Measures via Diffusion Processes
• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
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• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain