On the Decay of Correlations in the Random Field Ising Model

被引：14

作者：

Chatterjee, Sourav ^{[1
]}

机构：

[1] Stanford Univ, Dept Stat, Sequoia Hall,390 Serra Mall, Stanford, CA 94305 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2018年 / 362卷 / 01期

关键词：

INEQUALITIES; IDENTITIES;

D O I：

10.1007/s00220-018-3085-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information. This article proves the first quantitative version of the Aizenman-Wehr theorem. The proof introduces a new method for proving decay of correlations that may be interesting in its own right. A fairly detailed sketch of the main ideas behind the proof is also included.

引用

页码：253 / 267

页数：15

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