Dynamical behavior of the Niedermayer algorithm applied to Potts models

Abstract

In this work, we make a numerical study of the dynamic universality class of the Niedermayer algorithm applied to the two-dimensional Potts model with 2, 3, and 4 states. This algorithm updates clusters of spins and has a free parameter, E0, which controls the size of these clusters, such that E0=1 is the Metropolis algorithm and E0=0 regains the Wolff algorithm, for the Potts model. For −1<E0<0, only clusters of equal spins can be formed: we show that the mean size of the clusters of (possibly) turned spins initially grows with the linear size of the lattice, L, but eventually saturates at a given lattice size L˜, which depends on E0. For L≥L˜, the Niedermayer algorithm is in the same dynamic universality class of the Metropolis one, i.e, they have the same dynamic exponent. For E0>0, spins in different states may be added to the cluster but the dynamic behavior is less efficient than for the Wolff algorithm (E0=0). Therefore, our results show that the Wolff algorithm is the best choice for Potts models, when compared to the Niedermayer’s generalization.