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

We prove the rigorous lower bound z_sw≥α/ν 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.