Tempering Dynamics and Relaxation Times in the $3D$ Ising Model

TL;DR

This paper analyzes how tempering Monte Carlo methods affect relaxation times and critical slowing down in the 3D Ising model, showing that tempering reduces exponential slowing down to a power law in certain transitions.

Contribution

It demonstrates that tempering does not alter the critical slowing down exponent at T_c but reduces exponential slowing down to a power law in the cold phase transitions.

Findings

Tempering does not change the critical slowing down exponent at T_c.

Tempering reduces exponential slowing down to a power law in phase transition dynamics.

The flip-flop rate relates to surface tension in local dynamical schemes.

Abstract

We discuss the tempering Monte Carlo method, and its critical slowing down in the $3d$ Ising model. We show that at $T_c$ the tempering does not change the critical slowing down exponent $z$. We also discuss the exponential slowing down for the transition from the plus to the minus state in the cold phase, and we show that tempering reduces it to a power law slowing down. We discuss the relation of the flip-flop rate to the surface tension for the local dynamical schemes.