Numerical simulations of the Ising model on the Union Jack lattice

TL;DR

This paper reviews and re-examines the Union Jack lattice Ising model, focusing on anisotropic sublattice magnetisations and addressing discrepancies in previous predictions through numerical simulations and proposed modifications.

Contribution

It provides a critical comparison of existing theoretical results with new numerical simulations and suggests modifications for accurate predictions of sublattice magnetisations.

Findings

Disagreements in sublattice magnetisation predictions

Non-zero antiferromagnetic results identified

Rotational variance observed in predictions

Abstract

This paper reviews the work of Wu and Lin on the Union Jack lattice Ising model. This model is of interest as it one of the few to display re-entrant phase transitions. Specifically we re-examine their result for the general anisotropic sublattice magnetisations, comparing these with the works of Vaks, Larkin and Ovchinnikov, and our own numerical simulations. We discuss the disagreements found in both sublattice predictions including non-zero antiferromagnetic results and a rotational variance. We will then suggest additional conditions and modified formulae that will allow valid results to be produced.