Zero-Temperature Stochastic Ising Model
نویسندگان
چکیده
We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or −1 to each site in Z, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, polls its 4 neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times t < ∞, but the cluster of a fixed site diverges (in diameter) as t → ∞; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states. Mathematics Subject Classification 2000: 60K35, 82C22, 82C20, 60J25.
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