Fluctuations of the Magnetization for Ising models on Erd\H{o}s-R\'enyi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field

Zakhar Kabluchko; Matthias Löwe; Kristina Schubert

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arXiv · 2012.08204

Fluctuations of the Magnetization for Ising models on Erd\H{o}s-R\'enyi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field

Zakhar Kabluchko·Matthias Löwe·Kristina Schubert

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Abstract

We continue our analysis of Ising models on the (directed) Erd\H{o}s-R\'enyi random graph $G(N,p)$. We prove a quenched Central Limit Theorem for the magnetization and describe the fluctuations of the log-partition function. In the current note we consider the low temperature regime $\beta>1$ and the case when an external magnetic field is present. In both cases, we assume that $p=p(N)$ satisfies $p^3N \to \infty$.

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Zakhar Kabluchko, Matthias Löwe, Kristina Schubert. 2020-12-15. Fluctuations of the Magnetization for Ising models on Erd\H{o}s-R\'enyi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field. https://arxiv.org/abs/2012.08204

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