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)}.