A CLT for the total energy of the two-dimensional critical Ising model

被引：1

作者：

Jiang, Jianping ^{[1
]}

机构：

[1] NYU Shanghai, NYU ECNU Inst Math Sci, 3663 Zhongshan Rd North, Shanghai 200062, Peoples R China

来源：

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS | 2020年 / 17卷 / 02期

关键词：

Ising model; total energy; critical; central limit theorem; MAGNETIZATION; LIMIT;

D O I：

10.30757/ALEA.v17-29

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：

Consider the Ising model on ([1, 2N] x [1, 2M])boolean AND Z(2) at critical temperature with periodic boundary condition in the horizontal direction and free boundary condition in the vertical direction. Let E-M,E- (N) be its total energy (or Hamiltonian). Suppose M is a function of N satisfying M >= N=(ln N)(alpha) for some alpha is an element of [0, 1). In particular, one may take M = N. We prove that E-M,E- (N) + 4 root 2M N - (4/pi)N ln N/root(32/pi)M N ln N converges weakly to a standard Gaussian distribution as N -> infinity.

引用

页码：759 / 773

页数：15

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