Dynamics of the One-Dimensional Ising Model without Detailed Balance Condition

TL;DR

This paper investigates an irreversible Markov chain Monte Carlo method for the 1D Ising model, showing it can reduce relaxation times and alter critical dynamics compared to traditional detailed balance approaches.

Contribution

It introduces a skew detailed balance condition for the 1D Ising model and demonstrates its effects on relaxation times and dynamical critical exponents.

Findings

Relaxation time is reduced using skew detailed balance.

Transition probabilities can change the dynamical critical exponent.

The method offers improved dynamical properties over detailed balance.

Abstract

We study an irreversible Markov chain Monte Carlo method based on a skew detailed balance condition for an one-dimensional Ising model. Dynamical behavior of the magnetization density is analyzed in order to understand the properties of this method. As a result, it is found theoretically that the relaxation time of the magnetization density is reduced by using some transition probabilities satisfying the skew detailed balance condition, in comparison to that with the corresponding transition probability with the detailed balance condition, and that one of the transition probabilities changes the dynamical critical exponent even with a local spin update.