Dynamics for spherical spin glasses: Gibbs distributed initial conditions

2025/03/30 by Amir Dembo, Eliran Subag, Dembo, Amir +1 · 1 citation
Physics and Astronomy · Materials Science · #Theoretical and Computational Physics #Material Dynamics and Properties #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2503.23342

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 T₀, in the replica-symmetric (RS) or 1-replica-symmetry-breaking (RSB) phase. For any T₀=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 T₀=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.

Cited by

• On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses

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