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arXiv · 2002.11372

Fluctuations for the partition function of Ising models on Erd\"os-R\'enyi random graphs

Zakhar Kabluchko·Matthias Löwe·Kristina Schubert
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Abstract

We analyze Ising/Curie-Weiss models on the Erd\H{o}s-R\'enyi graph with $N$ vertices and edge probability $p=p(N)$ that were introduced by Bovier and Gayrard [J.\ Statist.\ Phys., 72(3-4):643--664, 1993] and investigated in two previous articles by the authors. We prove Central Limit Theorems for the partition function of the model and -- at other decay regimes of $p(N)$ -- for the logarithmic partition function. We find critical regimes for $p(N)$ at which the behavior of the fluctuations of the partition function changes.

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Zakhar Kabluchko, Matthias Löwe, Kristina Schubert. 2020-02-26. Fluctuations for the partition function of Ising models on Erd\"os-R\'enyi random graphs. https://arxiv.org/abs/2002.11372

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