Erdős-Rényi随机图上Ising模型磁化的波动——低温和外磁场的状态

Pub Date : 2020-12-15 DOI:10.30757/alea.v19-21

Z. Kabluchko, Matthias Lowe, K. Schubert

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引用次数: 4

摘要

我们继续分析(有向)Erdős-Renyi随机图$G(N,p)$上的Ising模型。我们证明了磁化的一个淬灭中心极限定理，并描述了对数配分函数的涨落。在当前的说明中，我们考虑低温状态$\beta>1$和存在外部磁场的情况。在这两种情况下，我们都假设$p=p(N)$满足$p^3N \to \infty$。

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Fluctuations of the Magnetization for Ising models on Erdős-Rényi random graphs – the regimes of low temperature and external magnetic field

We continue our analysis of Ising models on the (directed) Erdős-Renyi 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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