Rigorous lower bound on the dynamic critical exponents of the Swendsen-Wang algorithm.

We prove the rigorous lower bound z sw ≥α/v for the dynamic critical exponent of the Swendsen-Wang algorithm. For two-dimensional q-state Potts models with q=2, 3, 4, this implies z sw ≥0, 2/5, 1. We present numerical data indicating that z sw =0.55±0.03, 0.89±0.05 for q=3, 4 (95% confidence limits, statistical errors only). The discrepancy for q=4 appears to be caused by multiplicative logarithmic corrections