Fluctuations of the Magnetization for Ising models on Erdős-Rényi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field

2020/12/15 by Kabluchko, Zakhar, Löwe, Matthias, Schubert, Kristina
#82B20 #82B44 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2012.08204

Abstract

We continue our analysis of Ising models on the (directed) Erdős-Rényi 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 β>1 and the case when an external magnetic field is present. In both cases, we assume that p=p(N) satisfies p³N → ∞.

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