SHARP THRESHOLDS FOR THE RANDOM-CLUSTER AND ISING MODELS

被引：14

作者：

Graham, Benjamin ^{[1
,2
]}

Grimmett, Geoffrey ^{[3
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Ecole Normale Super, DMA, F-75230 Paris 5, France

[3] Univ Cambridge, Ctr Math Sci, Stat Lab, Cambridge CB3 0WB, England

来源：

ANNALS OF APPLIED PROBABILITY | 2011年 / 21卷 / 01期

关键词：

Random-cluster model; Potts model; Ising model; percolation; box-crossing; influence; sharp threshold; colored random-cluster model; fuzzy Potts model; CRITICAL PROBABILITY; CRITICAL-BEHAVIOR; PHASE-TRANSITION; PERCOLATION; MAGNETIZATION; COEXISTENCE; UNIQUENESS;

D O I：

10.1214/10-AAP693

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point p(sd)(q) = root q/(1 + root q), the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.

引用

页码：240 / 265

页数：26

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