Phase transitions in spin systems without detailed balance

Abstract

Stochastic Ising models for phase transitions in magnetic systems satisfy the condition of detailed balance and thus they have the Gibbs states as stationary states. On the other hand, some spin systems which do not satisfy the condition of detailed balance can have nontrivial stationary states as a result of nonequilibrium phase transitions. In the present paper, the contact process of Harris and the reaction-diffusion processes of Dickman are studied as typical examples of this class. The survival probability σ( A) is introduced to study the stationary states. Some theorems are given for these processes.