Percolation of the site random-cluster model by Monte Carlo method.
Percolation of the site random-cluster model by Monte Carlo method.
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DOI：
10.1103/physreve.92.022127
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发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
Songsong Wang;Wanzhou Zhang;Chengxiang Ding
中科院分区：
文献类型：
--
作者：
Songsong Wang;Wanzhou Zhang;Chengxiang Ding
We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability Re, the percolating cluster density P∞, and the magnetic susceptibility per site χp, as well as two exponents, such as the thermal exponent yt and the fractal dimension yh of the percolating cluster. We find that for different exponents of cluster weight q=1.5, 2, 2.5, 3, 3.5, and 4, the numerical estimation of the exponents yt and yh are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identical. For larger values of q, we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.
