Irreversible simulated tempering

TL;DR

This paper introduces an irreversible simulated tempering algorithm that violates detailed balance, leading to faster relaxation dynamics and reduced autocorrelation times in Monte Carlo simulations of the 2D Ising model.

Contribution

The paper proposes a novel irreversible simulated tempering method based on skew detailed balance, improving sampling efficiency over traditional algorithms.

Findings

Relaxation dynamics change from diffusive to ballistic.

Autocorrelation time of magnetization is significantly reduced.

Method outperforms conventional detailed balance algorithms.

Abstract

An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is constructed based on the framework of the skew detailed balance condition. By applying this method to the ferromagnetic Ising model in two dimensions on a square lattice as a benchmark, the dynamical behavior of the inverse temperature and an autocorrelation function of the magnetization are studied numerically. It is found that the relaxation dynamics of the inverse temperature changes qualitatively from diffusive to ballistic by violating the detailed balance condition. Consequently, the autocorrelation time of magnetization is several times smaller than that for the conventional algorithm satisfying the detailed balance condition.