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November 2021 Fluctuations for the partition function of Ising models on Erdös–Rényi random graphs
Zakhar Kabluchko, Matthias Löwe, Kristina Schubert
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Ann. Inst. H. Poincaré Probab. Statist. 57(4): 2017-2042 (November 2021). DOI: 10.1214/20-AIHP1137

Abstract

We analyze Ising/Curie–Weiss models on the Erdős–Rényi graph with N vertices and edge probability p=p(N) that were introduced by Bovier and Gayrard (J. Stat. Phys. 72 (3–4) (1993) 643–664) and investigated in (J. Stat. Phys. 177 (1) (2019) 78–94) and (Kabluchko, Löwe and Schubert (2019)). 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.

Nous analysons les modéles d’Ising/Curie–Weiss sur le graphe Erdős–Rényi avec N sommets et probabilité d’arête p=p(N) introduits par Bovier et Gayrard (J. Stat. Phys. 72 (3–4) (1993) 643–664) et étudié dans (J. Stat. Phys. 177 (1) (2019) 78–94) et (Kabluchko, Löwe and Schubert (2019)). Nous montrons des théorèmes limite central pour la fonction de partition du modèle et – à autres régimes de p(N) – pour la fonction de partition logarithmique. Nous trouvons des régimes critiques pour p(N) en lequels le comportement des fluctuations de la fonction de partition change.

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Zakhar Kabluchko. Matthias Löwe. Kristina Schubert. "Fluctuations for the partition function of Ising models on Erdös–Rényi random graphs." Ann. Inst. H. Poincaré Probab. Statist. 57 (4) 2017 - 2042, November 2021. https://doi.org/10.1214/20-AIHP1137

Information

Received: 28 February 2020; Revised: 25 September 2020; Accepted: 3 December 2020; Published: November 2021
First available in Project Euclid: 20 October 2021

Digital Object Identifier: 10.1214/20-AIHP1137

Subjects:
Primary: 60F05 , 82B44
Secondary: 82B20

Keywords: central limit theorem , Dilute Curie–Weiss model , Fluctuations , Ising model , Partition function , Random graphs

Rights: Copyright © 2021 Association des Publications de l’Institut Henri Poincaré

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Vol.57 • No. 4 • November 2021
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