Competing Glauber and Kawasaki Dynamics

TL;DR

This paper investigates a kinetic Ising model with competing Glauber and Kawasaki dynamics using a quantum master equation, revealing how correlation lengths depend on temperature and process probabilities.

Contribution

It introduces a quantum formulation to analyze the interplay of Glauber and Kawasaki dynamics in a kinetic Ising model, deriving exact relations to a Ginzburg Landau functional.

Findings

Correlation length depends on temperature and process probability p

Correlation length vanishes at finite temperature with spin flip processes

Strong correlations persist at all temperatures in exchange-dominated regime

Abstract

Using a quantum formulation of the master equation we study a kinetic Ising model with competing stochastic processes: the Glauber dynamics with probability $p$ and the Kawasaki dynamics with probability $1 - p$. Introducing explicitely the coupling to a heat bath and the mutual static interaction of the spins the model can be traced back exactly to a Ginzburg Landau functional when the interaction is of long range order. The dependence of the correlation length on the temperature and on the probability $p$ is calculated. In case that the spins are subject to flip processes the correlation length disappears for each finite temperature. In the exchange dominated case the system is strongly correlated for each temperature.