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arXiv · 2207.12247

Monotonicity of Ursell functions in the Ising model

Federico Camia·Jianping Jiang·Charles M. Newman
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Abstract

In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions $u_{2k}$ satisfy: $(-1)^{k-1}u_{2k}$ is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field $h$: its closest zero to the origin (in the variable $h$) moves towards the origin as an arbitrary interaction increases.

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BibTeXRIS

Federico Camia, Jianping Jiang, Charles M. Newman. 2022-07-25. Monotonicity of Ursell functions in the Ising model. https://doi.org/10.1007/s00220-023-04693-x

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