# Complex-Temperature Singularities of Ising Models

## TL;DR

This paper explores the complex-temperature phase diagrams and singularities of various two-dimensional Ising models, including higher-spin and external magnetic field cases, using partition function zeros and series analysis.

## Contribution

It provides new insights into the complex-temperature properties and phase diagrams of 2D Ising models, including exact results and zero analyses for higher-spin and magnetic field cases.

## Key findings

- Elucidation of complex-T phase diagrams for higher-spin Ising models.
- Exact results for phase diagrams at specific magnetic field values.
- Determination of susceptibility exponents at singularities.

## Abstract

We report new results on complex-temperature properties of Ising models. These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e, $3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase diagrams of the higher-spin 2D Ising models, using calculations of partition function zeros. Finally, we investigate the 2D Ising model in an external magnetic field, mapping the complex--$T$ phase diagram and exploring various singularities therein. For the case $\beta H=i\pi/2$, we give exact results on the phase diagram and obtain susceptibility exponents $\gamma'$ at various singularities from low-temperature series analyses.