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

Abstract

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,M 2 = z int,S 2 = 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 .