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arXiv · 2008.07256

Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph

Sheng Fang·Zongzheng Zhou·Youjin Deng
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Abstract

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.

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Sheng Fang, Zongzheng Zhou, Youjin Deng. 2020-08-17. Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph. https://doi.org/10.1103/physreve.103.012102

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