On the stochastic dynamics of disordered spin models

TL;DR

This paper investigates the stochastic dynamics of disordered spin models, deriving fluctuation-dissipation relations in equilibrium and proposing a formalism for approximate dynamics on complex graphs.

Contribution

It introduces a fluctuation principle for multi-time correlations and responses, and develops a formalism for approximate dynamic equations in disordered spin systems.

Findings

Derived fluctuation-dissipation relations for equilibrium systems.

Proposed a formalism for approximate dynamics on random graphs.

Discussed potential modifications of relations out of equilibrium.

Abstract

In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs.