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

TL;DR

This paper analyzes the complex-temperature zeros of the partition function for 2D higher-spin Ising models, revealing insights into their phase diagrams and proposing a conjecture on magnetization divergences related to zeros.

Contribution

It introduces calculations of partition function zeros for higher-spin 2D Ising models and proposes a new conjecture on the structure of these zeros and their relation to phase transitions.

Findings

Zeros form arcs in the complex-temperature plane.

Support for the conjecture that magnetization divergences occur at arc endpoints.

Number of arcs scales as 4 times the square of the spin minus 2.

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 $x$.