Deng Youjin, Zhang Wei, Garoni Timothy M, Sokal Alan D, Sportiello Andrea
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Feb;81(2 Pt 1):020102. doi: 10.1103/PhysRevE.81.020102. Epub 2010 Feb 10.
We introduce several infinite families of critical exponents for the random-cluster model and present scaling arguments relating them to the k -arm exponents. We then present Monte Carlo simulations confirming these predictions. These exponents provide a convenient way to determine k -arm exponents from Monte Carlo simulations. An understanding of these exponents also leads to a radically improved implementation of the Sweeny Monte Carlo algorithm. In addition, our Monte Carlo data allow us to conjecture an exact expression for the shortest-path fractal dimension d(min) in two dimensions: d(min)=over ?(g+18)/(32 g) , where g is the Coulomb-gas coupling, related to the cluster fugacity q via q=2+2 cos(gpi/2) with 2< or =g< or =4 .
我们介绍了随机簇模型的几个无穷族临界指数，并给出了将它们与k臂指数相关联的标度论证。然后我们给出了蒙特卡罗模拟，证实了这些预测。这些指数提供了一种从蒙特卡罗模拟确定k臂指数的便捷方法。对这些指数的理解还导致了Sweeny蒙特卡罗算法的显著改进。此外，我们的蒙特卡罗数据使我们能够推测二维中最短路径分形维数d(min)的精确表达式：d(min)=[根号下](g + 2)(g + 18)/(32g) ，其中g是库仑气体耦合，通过q = 2 + 2 cos(gπ/2) 与簇逸度q相关，2 ≤ g ≤ 4 。
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