A DISCRETE VARIATIONAL PROBLEM RELATED TO ISING DROPLETS AT LOW-TEMPERATURES

Authors
NEVES EJ
Citation
Ej. Neves, A DISCRETE VARIATIONAL PROBLEM RELATED TO ISING DROPLETS AT LOW-TEMPERATURES, Journal of statistical physics, 80(1-2), 1995, pp. 103-123
Citations number
9
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Journal of statistical physics → ACNP
ISSN journal
00224715
Volume
80
Issue
1-2
Year of publication
1995
Pages
103 - 123
Database
ISI
SICI code
0022-4715(1995)80:1-2<103:ADVPRT>2.0.ZU;2-E
Abstract
We consider a variational problem on the d-dimensional lattice Z(d) wh ich has applications in the study of the metastable behavior of the st ochastic Ising model. The problem, an isoperimetric one, is to iind wh at is the smallest area a finite subset of Z(d) can have restricted to three classes of subsets of Z(d). If phi is one of these subsets, we define its volume as the number of points in it and its area as the nu mber of pairs of points in Z(d) which are neighbors and such that only one of them belongs to phi.