Faizi Fahim, Deligiannidis George, Rosta Edina
Department of Mathematics, King's College London, Strand WC2R 2LS, SE1 1DB, London, U.K.
Department of Statistics, University of Oxford, 24-29 St Giles', OX1 3LB, Oxford, U.K.
J Chem Theory Comput. 2020 Apr 14;16(4):2124-2138. doi: 10.1021/acs.jctc.9b01135. Epub 2020 Mar 17.
We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metropolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from ≈ 1 to ≈ 1/2. In addition, we have generalized an irreversible Metropolis-Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ 2011, 240, 410] for the mean field Ising 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 the mixing time at high temperatures.
我们在此展示了两种适用于一般离散状态系统的不可逆马尔可夫链蒙特卡罗算法。其中一种算法基于离散状态的随机扫描吉布斯采样器，另一种基于其改进版本——大都会化吉布斯采样器。我们展示的算法将提升框架与倾斜的细致平衡条件相结合，并构建满足平衡条件的不可逆马尔可夫链。我们已将我们的算法应用于一维四态Potts模型。磁化强度和能量密度的积分自相关时间表明动力学标度指数从≈1降至≈1/2。此外，我们推广了一种具有倾斜细致平衡的不可逆梅特罗波利斯-黑斯廷斯算法，该算法最初由图里琴等人[2011, 240, 410]针对平均场伊辛模型引入，现在可轻松应用于一般的经典自旋系统；应用于一维四态Potts模型表明在高温下混合时间减少了平方根。
