Collective Monte Carlo Updating for Spin Systems

A Monte Carlo algorithm is presented that updates large clusters of spins simultaneously in systems at and near criticality. We demonstrate its efficiency in the two-dimensional $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ $\sigma$ models for $n=1\mathrm{}$ (Ising) and $n=2\mathrm{}$ ($x-y$) at their critical temperatures, and for $n=3\mathrm{}$ (Heisenberg) with correlation lengths around 10 and 20. On lattices up to ${128}^2$ no sign of critical slowing down is visible with autocorrelation times of 1-2 steps per spin for estimators of long-range quantities.