Percolation effects in the Fortuin-Kasteleyn Ising model on the complete graph
| Autor: | Zongzheng Zhou, Youjin Deng, Sheng Fang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Statistical Mechanics (cond-mat.stat-mech) Complete graph FOS: Physical sciences 01 natural sciences Condensed Matter::Disordered Systems and Neural Networks 010305 fluids & plasmas Distribution (mathematics) Percolation 0103 physical sciences Exponent Spin model Condensed Matter::Statistical Mechanics Ising model Configuration space Statistical physics 010306 general physics Scaling Condensed Matter - Statistical Mechanics |
| Popis: | 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. 9 pages, 12 figures |
| Databáze: | OpenAIRE |
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