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)}.
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Received: 20 February 1996 / In revised form: 15 June 1996
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Dehghanpour, P., Schonmann, R. A nucleation-and-growth model. Probab Theory Relat Fields 107, 123–135 (1997). https://doi.org/10.1007/s004400050079
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DOI: https://doi.org/10.1007/s004400050079
- Mathematics Subject classification (1991): 60K35
- 82A05