Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

TL;DR

This paper provides a comprehensive analysis of the full time evolution of a nonequilibrium Ising chain coupled to different thermal baths, revealing novel oscillatory decay behaviors and detailed correlation dynamics.

Contribution

It offers the first complete solution for the kinetics of a far-from-equilibrium Ising chain, including magnetization, correlation functions, and probability distributions.

Findings

Oscillatory decay into steady state observed.

Explicit time dependence of magnetization derived.

Correlation functions computed for specific initial conditions.

Abstract

The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetisation, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship to a reaction-diffusion model with pair annihilation and creation.