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 O(n) σ models for $n=1$ (Ising) and $n=2$ (x-y) at their critical temperatures, and for $n=3$ (Heisenberg) with correlation lengths around 10 and 20. On lattices up to 128² no sign of critical slowing down is visible with autocorrelation times of 1-2 steps per spin for estimators of long-range quantities.