Order-Parameter Flow in the SK Spin-Glass II: Inclusion of Microscopic Memory Effects

TL;DR

This paper extends a dynamical replica theory for the SK spin-glass to include microscopic memory effects via a joint spin-field distribution, accurately capturing relaxation phenomena and slowing down observed in simulations.

Contribution

It introduces a dynamic order parameter function to incorporate microscopic memory effects into the theory, improving its accuracy over previous models.

Findings

Accurately describes relaxation phenomena in SK spin-glass.

Captures the slowing down of dynamics observed in simulations.

The extended theory is either exact or a very good approximation.

Abstract

We develop further a recent dynamical replica theory to describe the dynamics of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution equations for macroscopic order parameters. We show how microscopic memory effects can be included in the formalism through the introduction of a dynamic order parameter function: the joint spin-field distribution. The resulting formalism describes very accurately the relaxation phenomena observed in numerical simulations, including the typical overall slowing down of the flow that was missed by the previous simple two-parameter theory. The advanced dynamical replica theory is either exact or a very good approximation.