Fluctuations for block spin Ising models

Electronic Communications in Probability

Matthias Löwe¹ 

关键词: Ising model;    Curie-Weiss model;    fluctuations;    Central Limit Theorem;    block model;   

DOI  :  10.1214/18-ECP161

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We analyze the high temperature fluctuations of the magnetization of the so-called Ising block model. This model was recently introduced by Berthet et al. in [2]. We prove a Central Limit Theorems (CLT) for the magnetization in the high temperature regime. At the same time we show that this CLT breaks down at a line of critical temperatures. At this line we prove a non-standard CLT for the magnetization.

【 授权许可】

CC BY