A NUCLEATION-AND-GROWTH MODEL

We consider the following simple nucleation-and-growth model. On the l attice Z(d), Starting with all sites unoccupied, a site becomes occupi ed at rate e(-beta Gamma) if it has no occupied neighbors, at rate eps ilon=e(-beta gamma) if it has 1 occupied neighbor, and at rate 1 if it has 2 or more occupied neighbors. Occupied sites remain occupied fore ver. The parameters Gamma greater than or equal to gamma are fixed, an d we are interested in the behavior of the system as beta-->infinity. We show that the relaxation time of this system scales as e(beta Kc), where K-c=max{gamma,(Gamma+gamma)/(d+1)}.