A nucleation-and-growth model

Summary. 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 ^−ℬΓ if it has no occupied neighbors, at rate ɛ= e ^−βγ 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 Γ≧γ are fixed, and we are interested in the behavior of the system as β→∞. We show that the relaxation time of this system scales as e ^βκc , where κ _c = max {γ,( Γ + γ)/(d+1)}. Received: 20 February 1996 / In revised form: 15 June 1996