Variational approach to the scaling function of the 2D Ising model in a magnetic field

TL;DR

This paper uses a variational corner transfer matrix method to accurately compute the universal scaling function of the 2D Ising model in a magnetic field, confirming theoretical predictions and previous results.

Contribution

It introduces a high-precision numerical approach that validates field theory results and enhances understanding of the 2D Ising model's scaling behavior in a magnetic field.

Findings

Excellent agreement with field theory results

High numerical precision demonstrates method's effectiveness

Confirms known analytical results for magnetic susceptibility

Abstract

The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.