Abstract:We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperature $T$, for spherical mixed $p$-spin disordered mean-field models, initialized according to a Gibbs measure for temperature $T_0$, in the replica-symmetric (RS) or $1$-replica-symmetry-breaking (RSB) phase. For any $T_0=T$ above the dynamical phase transition point $T_c^{\rm dyn}$ the resulting stationary relaxation dynamics coincide with the FDT solution for these equations, while for lower $T_0=T$ in the $1$-RSB phase, the relaxation dynamics coincides with the FDT solution, now concentrated on the single spherical band within the Gibbs measure's support on which the initial point lies.
From: Eliran Subag [view email]
[v1]
Sun, 30 Mar 2025 07:08:53 UTC (64 KB)
[v2]
Sat, 12 Apr 2025 11:01:57 UTC (66 KB)
[v3]
Wed, 8 Jul 2026 06:39:21 UTC (74 KB)
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