Ding Chengxiang, Wang Yancheng, Li Yang
Department of Applied Physics, Anhui University of Technology, Maanshan 243002, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 1):021125. doi: 10.1103/PhysRevE.86.021125. Epub 2012 Aug 22.
We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q = 1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al. [J. Phys. A 39, 15083 (2006)]. For the q = 2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is s(c) = 0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.
我们给出了蝴蝶结晶格上Potts模型的确切临界边界。对于q = 1的情况，临界边界给出了这些晶格上键渗流的阈值，这与Ziff等人[《物理学报A》39, 15083 (2006)]给出的结果完全一致。对于蝴蝶结A晶格上的q = 2 Potts模型，临界点与该晶格上已精确求解的伊辛模型的临界点一致。此外，我们对具有非整数q的蝴蝶结A晶格上的Potts模型进行了广泛的蒙特卡罗模拟。我们精确到七位有效数字的数值结果与理论预测一致。我们还模拟了蝴蝶结A晶格上的位点渗流，阈值为s(c) = 0.5479148(7)。在键渗流和位点渗流的模拟中，我们发现蝴蝶结A晶格上渗流模型的形状相关性质与各向同性晶格的性质有些不同，这可能是由晶格的各向异性引起的。
