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 and its efficiency is demonstrated in the two-dimensional $\mathrm{O}(n)$ $\ensuremath{\sigma}$ models.

Abstract

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 $\mathrm{O}(n)$ $\ensuremath{\sigma}$ models for $n=1$ (Ising) and $n=2$ ($x\ensuremath{-}y$) at their critical temperatures, and for $n=3$ (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.