CRITICAL-DYNAMICS OF CLUSTER ALGORITHMS IN THE DILUTE ISING-MODEL

Autocorrelation times for thermodynamic quantities at T(C) are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation times decrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for which increasing autocorrelation times are expected.