Deng Youjin, Qian Xiaofeng, Blöte Henk W J
Department of Modern Physics, Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230027, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036707. doi: 10.1103/PhysRevE.80.036707. Epub 2009 Sep 30.
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full-cluster decomposition of random-cluster configurations. We explore the critical dynamics of this algorithm for several two-dimensional Potts and random-cluster models. For integer q, the single-cluster algorithm can be reduced to the Wolff algorithm, for which case we find that the autocorrelation functions decay almost purely exponentially, with dynamic exponents z(exp)=0.07 (1), 0.521 (7), and 1.007 (9) for q=2, 3, and 4, respectively. For noninteger q, the dynamical behavior of the single-cluster algorithm appears to be very dissimilar to that of the SWCM algorithm. For large critical systems, the autocorrelation function displays a range of power-law behavior as a function of time. The dynamic exponents are relatively large. We provide an explanation for this peculiar dynamic behavior.
我们制定了一种用于模拟随机簇模型的单簇蒙特卡罗算法。该算法是将用于q态Potts模型的沃尔夫单簇方法推广到q>1的非整数值情况。其关于静态量的结果与现有的斯文森 - 王 - 查耶斯 - 马赫塔（SWCM）算法的结果吻合良好，后者涉及随机簇构型的完全簇分解。我们研究了该算法在几种二维Potts模型和随机簇模型中的临界动力学。对于整数q，单簇算法可简化为沃尔夫算法，在这种情况下我们发现，对于q = 2、3和4，自相关函数几乎纯粹呈指数衰减，动态指数z(exp)分别为0.07(1)、0.521(7)和1.007(9)。对于非整数q，单簇算法的动力学行为似乎与SWCM算法的动力学行为非常不同。对于大型临界系统，自相关函数随时间呈现出一系列幂律行为。动态指数相对较大。我们对这种奇特的动力学行为给出了解释。
