论文标题
Lee-Yang Zeros的运动
Motion of Lee-Yang zeros
论文作者
论文摘要
我们考虑具有铁磁对相互作用和复杂外部场的Ising模型的分区函数的零。在假设具有严格正相互作用的图形的假设下，我们在固定边缘处更改相互作用（用$ t $表示）。众所周知，每个零都是单调的（增加或减少）$ t $；我们证明它的运动是局部的：任何两个不同的零的轨迹都是不一致的。如果基础图是一个完整的图形，并且所有交互都采用相同的值$ t \ geq 0 $（即居里 - 韦斯型模型），我们证明所有主要的零（$ i [0，π/π/2）中的所有主要零以$ t $严格降低。
We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive interactions is connected, we vary the interaction (denoted by $t$) at a fixed edge. It is already known that each zero is monotonic (either increasing or decreasing) in $t$; we prove that its motion is local: the entire trajectories of any two distinct zeros are disjoint. If the underlying graph is a complete graph and all interactions take the same value $t\geq 0$ (i.e., the Curie-Weiss model), we prove that all the principal zeros (those in $i[0,π/2)$) decrease strictly in $t$.
