A Markov Chain Monte Carlo Study of the Beach Model
2000, v.6, Issue 3, 345-369
We study the beach model introduced by Burton and Steif. The model is an example of a strongly irreducible subshift of finite type which, when the parameter of the model exceeds a critical value, has more than one measure of maximal entropy. We are interested in the critical value and how it depends on dimension. By way of simulations, we find that the critical value seems to be decreasing as a function of the dimension. We also present a conjecture for the whereabouts of the critical value in 2 dimensions. Our simulations are made with Markov chain Monte Carlo methods. For some parameter values and sizes of systems we are able to use the Propp - Wilson algorithm for exact simulation. For other combinations of parameter value and size we use a variant of the Swendsen - Wang algorithm.
Keywords: Markov chain,Monte Carlo simulations,beach model,Propp - Wilson algorithm,Swendsen - Wang algorithm