Scaling and universality in the 2D Ising model with a magnetic field

TL;DR

This paper numerically computes the scaling function of the 2D Ising model with a magnetic field on square and triangular lattices, confirming universality and scaling hypotheses with high precision data.

Contribution

It introduces a high-precision numerical approach using Baxter's corner transfer matrix and Aharony-Fisher variables to study the 2D Ising model away from criticality.

Findings

Results confirm all scaling and universality predictions.

Excellent agreement with field theory and exact results.

High-precision data supports longstanding theoretical predictions.

Abstract

The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approach. The use of the Aharony-Fisher non-linear scaling variables allowed us to perform calculations sufficiently away from the critical point to obtain very high precision data, which convincingly confirm all predictions of the scaling and universality hypotheses. The results are in excellent agreement with the field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with the classic analytic results for the magnetic susceptibility by Barouch, McCoy, Tracy and Wu, recently enhanced by Orrick, Nickel, Guttmann and Perk.