Single cluster dynamics for the infinite range O(n) model

This paper presents a study of Wolff's single cluster acceleration algorithm for O(n) models in the infinite range or mean-field limit. Numerical results for n = 2, 3 and 4 are consistent with the complete elimination of critical slowing down. Also a heuristic argument is advanced to support the value of z = 0 for the dynamic critical exponent. A new cluster growth algorithm is formulated for the infinite range model that has optimal efficiency of O(inN) in the system size N for the Swendsen-Wang update scheme. Using an asymptotically correct version of this cluster method, we are able to perform simulations for the Wolff update scheme up to 262,144 spins for 105 time steps for the O(N) models.