Dynamical Replica Theory for Disordered Spin Systems

TL;DR

This paper introduces a novel dynamical replica theory for disordered spin systems that accurately models their finite-time behavior, bridging equilibrium and non-equilibrium states, and is validated on spin-glass models.

Contribution

The paper develops a new dynamical replica theory that provides an exact description of finite-time dynamics in disordered spin systems, including spin-glass models.

Findings

Accurately describes finite-time dynamics of spin glasses

Matches numerical experiments very well

Unifies equilibrium and non-equilibrium states in the theory

Abstract

We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical replica theory which, in the case of detailed balance, incorporates equilibrium replica theory as a stationary state. The theory is exact in various limits. We apply our theory to both the symmetric- and the non-symmetric Sherrington-Kirkpatrick spin-glass, and show that it describes the (numerical) experiments very well.