Poisson approximations for the Ising model

被引：2

作者：

Coupier, D ^{[1
]}

机构：

[1] Univ Lille, Ecole Polytech, F-59655 Villeneuve Dascq, France

来源：

JOURNAL OF STATISTICAL PHYSICS | 2006年 / 123卷 / 02期

关键词：

Poisson approximation; Ising model; ferromagnetic interaction; Stein-Chen method;

D O I：

10.1007/s10955-006-9033-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A d-dimensional Ising model on a lattice torus is considered. As the size n of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field a = a(n) tends to -infinity and the pair potential b remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case.

引用

页码：473 / 495

页数：23

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