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

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.