Open Access
2018 Fluctuations for block spin Ising models
Matthias Löwe, Kristina Schubert
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP161


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.


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Matthias Löwe. Kristina Schubert. "Fluctuations for block spin Ising models." Electron. Commun. Probab. 23 1 - 12, 2018.


Received: 22 June 2018; Accepted: 6 August 2018; Published: 2018
First available in Project Euclid: 1 September 2018

zbMATH: 1402.60027
MathSciNet: MR3852267
Digital Object Identifier: 10.1214/18-ECP161

Primary: 60F05 , 60G09 , 82B05

Keywords: block model , central limit theorem , Curie-Weiss model , Fluctuations , Ising model

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