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

26 Feb 2020 Kabluchko Zakhar Löwe Matthias Schubert Kristina

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... (read more)

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