A Fast Serial Algorithm for the Finite Temperature Quenched Potts Model

<p> An efficient serial algorithm for finite temperature, quenched Potts model simulations of domain evolution has been developed. This '' <em> n </em> &hyphen;fold way'' algorithm eliminates unsuccessful spin flip attempts <em> a prior </em> i by flipping sites with a frequency proportional to their site activity, defined as the sum of the probability of success for every possible spin flip at that site. Finite temperature efficiency for high&hyphen;spin degeneracy systems is achieved by utilizing a new, analytical expression for the portion of the site activity due to flips to non-neighbor spin values. Hence, to determine the activity of a site, only flips to the nearest neighbor spin values need be considered individually; all other flips are evaluated in a single expression. A complexity analysis of this algorithm gives the dependence of computing time on system parameters and on simulation progress. While a conventional Potts model algorithm has a constant computing time per simulation timestep, the <em> n </em> -fold way algorithm increases in efficiency as domain coarsening progresses. Computer experiments confirm the complexity analysis results and indicate that the n-fold way algorithm is much more efficient than the conventional algorithm even at high fractions of the critical temperature.</p>