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 zint,N = zint,E = zint,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 zint,M2 = zint,S2 = 0.443 ± 0.005 ± 0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find zexp ≈ 0.481. Our data are consistent with the Coddington–Baillie conjecture zSW = β/ν ≈ 0.5183, especially if it is interpreted as referring to zexp. PACS codes: 05.50.+q, 05.10.Ln, 64.60.Cn, 64.60.Ht.