The Contact Process

Abstract

The contact process is the spin system in which S = Z^d and

$$ c(x,\eta ) = \left\{ {\begin{array}{*{20}c} {\lambda \sum\limits_{|y - x| = 1} {\eta (y)} } & {if{\text{ }}\eta (x) = 0,} \\ 1 & {f{\text{ }}\eta (x) = 1,} \\ \end{array} } \right. $$

((0.1))

where λ is a nonnegative parameter. One interpretation of this process is as a model for the spread of an infection. An individual at x ∈ S is infected if η(x) = 1 and healthy if η (x) = 0. Healthy individuals become infected at a rate which is proportional to the number of infected neighbors. Infected individuals recover at a constant rate, which is normalized to be 1.