Dynamic critical behavior of the Swendsen - Wang algorithm for the three-dimensional Ising model

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find z_int,N=z_int,E= z_int,E′=0.459±0.005±0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find z_int,M²=z_int, S₂=0.443±0.005±0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find z_exp≈0.481. Our data are consistent with the Coddington-Baillie conjecture z_SW=β/ν≈0.5183, especially if it is interpreted as referring to z_exp.