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.
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页码：240 / 265
页数：26
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