  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.
