Dynamics for spherical spin glasses: disorder dependent initial conditions. (English) Zbl 1456.82846
In the paper the authors investigated the thermodynamic (\(N\to\infty\)), long-time (\(t\to\infty\)), behavior of a class of systems composed of \(N\) Langevin particles interacting with each other through a random potential.
Namely, the thermodynamic limit of the empirical correlation and response functions is derived for spherical mixed p-spin disordered mean-field models, starting uniformly within one of the spherical bands on which (at low temperature) the Gibbs measure concentrates for the pure p-spin models and mixed perturbations of them. Moreover, the large time asymptotics of the corresponding coupled non-linear integro-differential equations is related to the geometric structure of the Gibbs measures (at low temperature), and derive their FDT (Fluctuation Dissipation Theorem) solution (at high temperature).
Reviewer: Utkir A. Rozikov (Tashkent)
MSC:
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 35R09 | Integro-partial differential equations |
| 45K05 | Integro-partial differential equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60F15 | Strong limit theorems |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
Keywords:
interacting random processes; disordered systems; statistical mechanics; Langevin dynamics; aging; spin Glass modelsReferences:
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