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

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.