Dynamical behavior of the Niedermayer algorithm applied to Potts models

TL;DR

This study numerically investigates the dynamic universality class of the Niedermayer algorithm applied to 2D Potts models with different states, comparing its efficiency and cluster behavior to established algorithms like Metropolis and Wolff.

Contribution

It provides a detailed numerical analysis of the Niedermayer algorithm's dynamic behavior and universality class for various parameters and states in the Potts model, highlighting its relation to other algorithms.

Findings

Niedermayer algorithm's cluster size saturates at a lattice-dependent scale.

For large lattices, Niedermayer's algorithm shares the same dynamic exponent as Metropolis.

Wolff algorithm remains the most efficient for 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 $\widetilde{L}$, which depends on $E_0$. For $L \geq \widetilde{L}$, 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.