Spin Systems

Abstract

A spin system is an interacting particle system in which each coordinate has two possible values, and only one coordinate changes in each transition. Throughout this chapter, the state space of the system will be taken to be X = {0, l}^s where S is a finite or countable set. There are numerous possible interpretations of the two possible values 0 and 1. The next three chapters deal with three classes of spin systems in which the transition mechanisms have a particular form, and each of these classes corresponds to a different interpretation for 0 and 1. In the stochastic Ising model, they represent the two possible spins of an iron atom (for example). In the case of the voter model, they denote two possible positions of a “voter” on some political issue. In the case of the contact process, 0 and 1 represent healthy and infected individuals respectively.