On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations

TL;DR

This paper investigates how small non-Hamiltonian perturbations affect the aging dynamics and stability of the mean-field glass phase in the SK model, revealing that aging persists under small perturbations but is destroyed by larger ones.

Contribution

It provides a detailed numerical analysis of the stability of the glass phase under non-Hamiltonian perturbations, highlighting differences from spherical models and discussing decay behaviors.

Findings

Aging survives small perturbations in the SK model.

Large perturbations destroy the aging phase.

Power law decay of observables is preserved for small perturbations.

Abstract

We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume we are observing a transient behavior the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power like decay is preserved. We also discuss the asymptotically large time region on small lattices.