Metastable lifetimes in a kinetic Ising model: Dependence on field and system size

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal power-law prefactors. Quantitative droplet-theory predictions are numerically verified, and small deviations are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite droplet density, vanishes logarithmically with system size. As a consequence the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.Comment: 18 pages single spaced. RevTex Version 3. FSU-SCRI-94-1

A Note on Percolation in a Voronoi Competition-Growth Model

We study a model in which two entities (e.g., plant species, political ideas, ...) compete for space on a plane, starting from randomly distributed seeds, and growing deterministically at possibly different rates. An entity which forms an infinite cluster is considered to dominate over the other (which then cannot percolate). We analyze the occurence of such a form of domination in situations in which one entity starts from a much larger density of seeds than the other one, but the latter one grows at a much faster rate than the former one. The model studied here generalizes the problem of Voronoi percolation. 1 Introduction Suppose that initially the seeds of two plant species A and B are randomly distributed on the plane and that the region occupied by each species starts to grow radially with constant speed vA and vB for the species A and B, respectively, starting from their seeds, so that after a relatively short time interval s, each seed A, or B, will be the center of a ball of ..