The Swendsen-Wang algorithm is a widely used MCMC algorithm for the
Potts model. In this talk I present recent results by J.T. Chayes,
P. Tetali and myself, establishing matching upper and lower bounds for
the mixing time on the torus, at the transition temperature $T_0$.
The upper bound is obtained by a comparison argument linking the
mixing time on a graph G to the product of the mixing time on induced
subgraphs. By contrast, the lower bound uses contour estimates
involving the so-called FK-representation of the model. Our results
significantly improve the previous lower bounds, and also supplement
them with a matching upper bound.

Lecture #10814

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