Comments on Sweeny and Gliozzi dynamics for simulations of Potts models in the Fortuin-Kasteleyn representation

TL;DR

This paper compares the correlation times of Sweeny and Gliozzi dynamics with other cluster algorithms in Potts and Ising models, showing similar critical behavior and addressing claims about their efficiency.

Contribution

It provides a detailed comparison of Sweeny and Gliozzi dynamics, demonstrating their similar critical slowing down and correcting previous claims about Gliozzi's efficiency.

Findings

Sweeny and Gliozzi dynamics exhibit similar critical behavior.

Gliozzi dynamics has critical slowing down comparable to other cluster methods.

Two-dimensional Ising and Potts models fit logarithmic size dependence.

Abstract

We compare the correlation times of the Sweeny and Gliozzi dynamics for two-dimensional Ising and three-state Potts models, and the three-dimensional Ising model for the simulations in the percolation prepresentation. The results are also compared with Swendsen-Wang and Wolff cluster dynamics. It is found that Sweeny and Gliozzi dynamics have essentially the same dynamical critical behavior. Contrary to Gliozzi's claim (cond-mat/0201285), the Gliozzi dynamics has critical slowing down comparable to that of other cluster methods. For the two-dimensional Ising model, both Sweeny and Gliozzi dynamics give good fits to logarithmic size dependences; for two-dimensional three-state Potts model, their dynamical critical exponent z is 0.49(1); the three-dimensional Ising model has z = 0.37(2).