Rigidity of the interface for percolation and random-cluster models
概率论
2007-05-23 v1 数学物理
math.MP
摘要
We study conditioned random-cluster measures with edge-parameter p and cluster-weighting factor q satisfying q \ge 1. The conditioning corresponds to mixed boundary conditions for a spin model. Interfaces may be defined in the sense of Dobrushin, and these are proved to be `rigid' in the thermodynamic limit, in three dimensions and for sufficiently large values of p. This implies the existence of non-translation-invariant (conditioned) random-cluster measures in three dimensions. The results are valid in the special case q=1, thus indicating a property of three-dimensional percolation not previously noted.
引用
@article{arxiv.math/0109103,
title = {Rigidity of the interface for percolation and random-cluster models},
author = {Guy Gielis and Geoffrey Grimmett},
journal= {arXiv preprint arXiv:math/0109103},
year = {2007}
}
备注
33 pages