A nucleation-and-growth model

We consider the following simple nucleation-and-growth model. On the lattice Z(d), Starting with all sites unoccupied, a site becomes occupied at rate e(-beta Gamma) if it has no occupied neighbors, at rate epsilon=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 forever. The parameters Gamma greater than or equal to gamma are fixed, and 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)}.