Zeros of the Partition Function for Higher--Spin 2D Ising Models

Abstract

We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the thermodynamic limit. Support is adduced for a conjecture that all divergences of the magnetisation occur at endpoints of arcs of zeros protruding into the FM phase. We conjecture that there are $4[s^2]-2$ such arcs for $s \ge 1$, where $[x]$ denotes the integral part of $x$.