论文标题
完整图上的fortuin-kasteleyn ising模型中的渗透效应
Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph
论文作者
论文摘要
fortuin-kasteleyn（fk）随机群集模型，可以从$ q $ - 状态potts旋转模型中精确映射，是一个相关的键渗透模型。通过广泛的蒙特卡洛模拟，我们研究了有限完整图，即平均场iSing模型的关键ISING模型（$ Q = 2 $）的FK键表示。我们提供了有力的数值证据，表明$ Q = 2 $的配置空间包含一个渐近消失的扇区，在该扇区中，数量与完整图上的关键不相关的键渗透（$ q = 1 $）中的数量显示出相同的有限尺寸缩放缩放。此外，我们观察到，在完整的配置空间中，FK Ising群集的集群大小分布的幂律行为除外，最大的群集由Fisher指数支配，以$ q = 1 $而不是$ q = 2 $，以$ q = 1 $。这证明了完整图上的FK Ising模型中的渗透效应。
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 behaviour 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.
