An efficient serial algorithm for finite temperature, quenched Potts model simulations of domain evolution has been developed. This ‘‘n‐fold way’’ algorithm eliminates unsuccessful spin flip attempts apriori 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‐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 n‐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.

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