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We present here two irreversible Markov chain Monte Carlo algorithms forgeneral discrete state systems, one of the algorithms is based on therandom-scan Gibbs sampler for discrete states and the other on its improvedversion, the Metropolized-Gibbs sampler. The algorithms we present incorporatethe lifting framework with skewed detailed balance condition and constructirreversible Markov chains that satisfy the balance condition. We have appliedour algorithms to 1D 4-state Potts model. The integrated autocorrelation timesfor magnetisation and energy density indicate a reduction of the dynamicalscaling exponent from $z \approx 1$ to $z \approx 1/2$. In addition, we havegeneralized an irreversible Metropolis-Hastings algorithm with skewed detailedbalance, initially introduced by Turitsyn et al. (2011) for the mean fieldIsing model, to be now readily applicable to classical spin systems in general;application to 1D 4-state Potts model indicate a square root reduction of themixing time at high temperatures.

Efficient Irreversible Monte Carlo samplers