# Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited

## TL;DR

This study investigates the dynamic critical behavior of the Swendsen-Wang algorithm applied to the 2D 3-state Potts model, revealing that the Li-Sokal bound is nearly sharp with a divergence in the ratio of autocorrelation time to specific heat.

## Contribution

The paper provides high-precision Monte Carlo results showing the near-sharpness of the Li-Sokal bound and the divergence behavior of the autocorrelation time ratio.

## Key findings

- Li-Sokal bound is almost sharp but not quite
- The ratio τ_{int,E} / C_H diverges as a small power or logarithm
- Autocorrelation times grow faster than specific heat near criticality

## Abstract

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$) is almost but not quite sharp. The ratio $\tau_{int,E} / C_H$ seems to diverge either as a small power ($\approx 0.08$) or as a logarithm.