A new look at the 2D Ising model from exact partition function zeros for large lattice sizes

TL;DR

This paper introduces a numerical method to locate partition function zeros in the complex beta plane for large 2D Ising lattices, providing insights into phase transitions and corrections to scaling.

Contribution

It presents a novel numerical approach for locating partition function zeros in large lattices and proposes a new method to evaluate scaling corrections using leading zeros.

Findings

Partition function zeros successfully located for lattices up to size 64x64.

The proposed correction evaluation method effectively uses only leading zeros.

Results enhance understanding of phase transition behavior in large 2D Ising models.

Abstract

A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data.