Abstract

This is a study of Monte Carlo simulations of ferromagnetic material using Ising and Potts spin models to ascertain selected properties of such material. It begins with a discussion of what spin models are and how they are used to simulate magnetic material, with particular attention to the use of cluster algorithms.

Most of this study reports results obtained by means of a simulation program developed by the author. The capabilities of this program are stated, with a discussion of how various quantities such as internal energy and the Binder cumulant are calculated. The program is validated by comparison with data produced by high temperature series expansions.

Using the Binder cumulant method and data obtained from many simulations the critical temperatures of the pure Ising model on a variety of lattices (square, triangular, honeycomb, cubic, diamond and 4d hypercubic) are derived.

The effect of site- and bond-dilution on the critical temperature of the Ising model on the square lattice is studied over a range of dilutions down to the site- and bond-percolation thresholds. Evidence is presented that the Binder cumulant method breaks down as the percolation threshold is approached.

The simulation program is then used to extract the critical exponent of the magnetization for the pure Ising model on square, triangular and honeycomb lattices, and for the 3-state Potts model on the square lattice.

Results reported in the literature for short-time critical dynamics in the Ising and  the 3-state Potts model are reproduced, and the same method is applied to the 4-state Potts model to obtain a new result for the short-time critical exponent, and an estimate for the dynamic critical exponent.

All results obtained using the simulation program are, where possible, compared to results published in the literature.

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