Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field

TL;DR

This paper employs the corner transfer matrix method to numerically analyze the Yang-Lee singularity in the 2D Ising model under a complex magnetic field, confirming theoretical predictions with high precision.

Contribution

It introduces a combined numerical and analytic approach to accurately locate the Yang-Lee singularity and validate conformal field theory predictions for the 2D Ising model.

Findings

Accurate estimation of the Yang-Lee singularity location.

Confirmation of the scaling function's behavior with conformal field theory.

Enhanced precision through series expansion integration.

Abstract

We study the 2D Ising model in a complex magnetic field in the vicinity of the Yang-Lee edge singularity. By using Baxter's variational corner transfer matrix method combined with analytic techniques, we numerically calculate the scaling function and obtain an accurate estimate of the location of the Yang-Lee singularity. The existing series expansions for susceptibility of the 2D Ising model on a triangular lattice by Chan, Guttmann, Nickel and Perk allowed us to substantially enhance the accuracy of our calculations. Our results are in excellent agreement with the Ising field theory calculations by Fonseca, Zamolodchikov and the recent work by Xu and Zamolodchikov. In particular, we numerically confirm an agreement between the leading singular behavior of the scaling function and the predictions of the ${\mathcal M}_{2/5}$ conformal field theory.