Competing Glauber and Kawasaki Dynamics

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.