Potts and percolation models on bowtie-type lattices

Details Potts and percolation models on bowtie-type lattices Potts and percolation models on bowtie-type lattices

2012-03-10

arxiv.org/abs/1203.2244v2

Physics

Condensed Matter

Statistical Mechanics

17 pages, 9 figures and 3 tables

Scientific paper

We give the exact critical frontier of the Potts model on the bowtie-type 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. For the q=2 Potts model on the 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 Potts model on the bowtie-A lattice with noninteger q. Our numerical results, which are accurate up to 7 significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on the 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 universality of the percolation model on the bowtie-A lattice breaks down. This may be caused by the anisotropy of the lattice.

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