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

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