Monotonicity of Ursell Functions in the Ising Model

摘要

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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