论文标题
Ising模型中Ursell函数的单调性
Monotonicity of Ursell functions in the Ising model
论文作者
论文摘要
在本文中，我们考虑具有铁磁相互作用的模型。我们证明ursell函数$ u_ {2k} $满意：$（ - 1）^{k-1} u_ {2k} $在每种交互中都在增加。作为一个应用程序，我们证明了Nishimori的1983年猜想和Griffiths关于ISING模型的分区功能，具有复杂的外部字段$ H $：它最接近的零（在变量$ H $中）向原点移动，作为任意交互的增加。
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.
