Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model
| dc.creator | Camia, F. | |
| dc.creator | De Santis, E. | |
| dc.creator | Newman, C. M. | |
| dc.date | 2001-03-07 | |
| dc.date.accessioned | 2026-07-07T04:40:33Z | |
| dc.date.available | 2026-07-07T04:40:33Z | |
| dc.description | 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 ${\bf Z}^2$, 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 $t< \infty$, but the cluster of a fixed site diverges (in diameter) as $t \to \infty$; 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. | |
| dc.description | 16 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0103050 | |
| dc.identifier | http://arxiv.org/abs/math/0103050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61058 | |
| dc.subject | Probability | |
| dc.subject | Statistical Mechanics | |
| dc.subject | 60K35, 82C22, 82C20, 60J25 | |
| dc.title | Clusters and Recurrence in the Two-Dimensional Zero-Temperature Stochastic Ising Model | |
| dc.type | text |