Dynamical behavior of the Niedermayer algorithm applied to Potts models

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, E 0 , which controls the size of these clusters, such that E 0 = 1 is the Metropolis algorithm and E 0 = 0 regains the Wolff algorithm, for the Potts model. For − 1 < E 0 < 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 E 0 . 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 E 0 > 0 , spins in different states may be added to the cluster but the dynamic behavior is less efficient than for the Wolff algorithm ( E 0 = 0 ). Therefore, our results show that the Wolff algorithm is the best choice for Potts models, when compared to the Niedermayer’s generalization.