PLANAR ISING MAGNETIZATION FIELD I. UNIQUENESS OF THE CRITICAL SCALING LIMIT

被引：39

作者：

Camia, Federico ^{[1
,2
]}

Garban, Christophe ^{[3
]}

Newman, Charles M. ^{[4
]}

机构：

[1] Vrije Univ Amsterdam, Dept Math, NL-1081 HV Amsterdam, Netherlands

[2] NYU Abu Dhabi, Abu Dhabi, U Arab Emirates

[3] ENS, CNRS, F-69364 Lyon, France

[4] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

ANNALS OF PROBABILITY | 2015年 / 43卷 / 02期

基金：

美国国家科学基金会;

关键词：

Planar Ising model; critical Ising model; continuum scaling limit; magnetization field; Euclidean field theory; conformal invariance; FK clusters; INFINITE CONFORMAL SYMMETRY; ERASED RANDOM-WALKS; CRITICAL PERCOLATION; INVARIANCE; CLUSTER; SLE; FLUCTUATIONS; BOUNDS; MODEL;

D O I：

10.1214/13-AOP881

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：

The aim of this paper is to prove the following result. Consider the critical Ising model on the resealed grid aZ(2), then the renormalized magnetization field Phi(a) := a(15/8)s Sigma(x is an element of aZ2)sigma(x)delta(x), seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a SE arrow 0. The limiting field is conformally covariant.

引用

页码：528 / 571

页数：44

共 57 条

[1] SUSCEPTIBILITY AND FLUCTUATIONS IN ISING FERROMAGNET [J].