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,
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.