Irreversible Simulated Tempering
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 on the basis of 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 qualitatively change from diffusive to ballistic on violating the detailed balance condition. Consequently, the autocorrelation time of the magnetization is several times smaller than that for the conventional algorithm satisfying the detailed balance condition.