Monte Carlo simulations for Ising spins with spin greater than 1/2 applied to the square and triangular lattices with antiferromagnetic interactions and comparing results using Kawasaki and Glauber dynamics

TL;DR

This paper provides a detailed guide on Monte Carlo simulation methods for higher-spin Ising models, comparing Kawasaki and Glauber dynamics on antiferromagnetic lattices, highlighting correct procedures and their impacts.

Contribution

It introduces a pedagogical approach for simulating higher-spin Ising models and compares two dynamics methods on specific lattice types, clarifying their differences and effects.

Findings

Correct simulation procedures are essential for accurate results.

Kawasaki and Glauber dynamics yield different behaviors in simulations.

Differences are demonstrated on square and triangular lattices for S=1.

Abstract

This paper has a pedagogical introduction. We describe the correct method for performing Monte Carlo simulations of Ising model systems with spin greater than one half. Correct and incorrect procedures are clearly outlined and the consequences of using the incorrect procedure are shown. The difference between Kawasaki and Glauber dynamics is then outlined and both methods are applied to the antiferromagnetic square and triangular lattices for S =1.