Monotonicity of Ursell Functions in the Ising Model

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.

Automated summary

In this paper, Ising models with ferromagnetic pair interactions are considered. The authors prove that the Ursell functions u(2k) are increasing in each interaction. As an application, a conjecture made by Nishimori and Griffiths in 1983 about the partition function of the Ising model with a complex external field is proven: the nearest zero to the origin (in the variable h) moves towards the origin as any interaction increases.