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

TL;DR

This study uses high-precision Monte Carlo simulations to analyze the dynamic critical behavior of the Swendsen-Wang algorithm for the 3D Ising model, providing precise estimates of autocorrelation exponents.

Contribution

It offers the first high-precision estimates of the dynamic critical exponents for the Swendsen-Wang algorithm in three dimensions, confirming theoretical conjectures.

Findings

Estimated autocorrelation exponents for energy-like observables (~0.459)

Estimated autocorrelation exponents for susceptibility-like observables (~0.443)

Exponential autocorrelation time exponent (~0.481)

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} \approx 0.481. Our data are consistent with the Coddington-Baillie conjecture z_{SW} = \beta/\nu \approx 0.5183, especially if it is interpreted as referring to z_{exp}.