Ising (conformal) fields and cluster area measures

被引：18

作者：

Camia, Federico ^{[1
]}

Newman, Charles M. ^{[2
]}

机构：

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

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

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2009年 / 106卷 / 14期

基金：

美国国家科学基金会;

关键词：

continuum scaling limit; critical Ising model; FK clusters; SLE; CLE; CRITICAL PERCOLATION; SCALING LIMITS; MODEL;

D O I：

10.1073/pnas.0900700106

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by using Schramm-Loewner Evolution clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical Fortuin-Kasteleyn clusters and the random field is a convergent sum of the area measures with random signs. Extensions to off-critical scaling limits, to d = 3, and to Potts models are also considered.

引用

页码：5457 / 5463

页数：7

共 41 条

[1] Holder regularity and dimension bounds for random curves [J].