Dynamics for spherical spin glasses: disorder dependent initial conditions

Abstract

We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed $p$-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the Gibbs measure concentrates at low temperature for the pure $p$-spin models and mixed perturbations of them. We further relate the large time asymptotics of the resulting coupled non-linear integro-differential equations, to the geometric structure of the Gibbs measures (at low temperature), and derive their FDT solution (at high temperature).

arXiv commentTo appear in J. Stat. Phys

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Cited by in corpus (2)

• Dynamical Instantons and Activated Processes in Mean-Field Glass Models
• High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Models