Fang Sheng, Zhou Zongzheng, Deng Youjin
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics, Monash University, Clayton, Victoria 3800, Australia.
Phys Rev E. 2021 Jan;103(1-1):012102. doi: 10.1103/PhysRevE.103.012102.
The Fortuin-Kasteleyn (FK) random-cluster model, which can be exactly mapped from the q-state Potts spin model, is a correlated bond percolation model. By extensive Monte Carlo simulations, we study the FK bond representation of the critical Ising model (q=2) on a finite complete graph, i.e., the mean-field Ising model. We provide strong numerical evidence that the configuration space for q=2 contains an asymptotically vanishing sector in which quantities exhibit the same finite-size scaling as in the critical uncorrelated bond percolation (q=1) on the complete graph. Moreover, we observe that, in the full configuration space, the power-law behavior of the cluster-size distribution for the FK Ising clusters except the largest one is governed by a Fisher exponent taking the value for q=1 instead of q=2. This demonstrates the percolation effects in the FK Ising model on the complete graph.
福尔图因 - 卡斯特莱因（FK）随机簇模型是一种相关键渗流模型，它可以从q态Potts自旋模型精确映射得到。通过大量的蒙特卡罗模拟，我们研究了有限完全图上临界伊辛模型（q = 2）的FK键表示，即平均场伊辛模型。我们提供了有力的数值证据，表明q = 2的构型空间包含一个渐近消失的扇区，其中的量表现出与完全图上临界不相关键渗流（q = 1）相同的有限尺寸标度。此外，我们观察到，在整个构型空间中，除最大的FK伊辛簇外，FK伊辛簇的簇尺寸分布的幂律行为由取值为q = 1而非q = 2的费希尔指数控制。这证明了完全图上FK伊辛模型中的渗流效应。
