Percolation transitions in two dimensions
| dc.creator | Feng, Xiaomei | |
| dc.creator | Deng, Youjin | |
| dc.creator | Blote, Henk W. J. | |
| dc.date | 2009-01-10 | |
| dc.date.accessioned | 2026-07-07T12:28:17Z | |
| dc.date.available | 2026-07-07T12:28:17Z | |
| dc.description | We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced lattices with nearest-neighbor bonds, and the square lattice with nearest- and next-nearest-neighbor bonds. Results are presented for the bond-percolation thresholds of the kagome and diced lattices, and the site-percolation thresholds of the square, honeycomb and diced lattices. We also include the bond- and site-percolation thresholds for the square lattice with nearest- and next-nearest-neighbor bonds. We find that corrections to scaling behave according to the second temperature dimension $X_{t2}=4$ predicted by the Coulomb gas theory and the theory of conformal invariance. In several cases there is evidence for an additional term with the same exponent, but modified by a logarithmic factor. Only for the site-percolation problem on the triangular lattice such a logarithmic term appears to be small or absent. The amplitude of the power-law correction associated with $X_{t2}=4$ is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems. | |
| dc.description | 6 pages, 1 figure, 3 tables | |
| dc.identifier | https://arxiv.org/abs/0901.1370 | |
| dc.identifier | http://arxiv.org/abs/0901.1370 | |
| dc.identifier | Phy. Rev. E 78 031136 (2008) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215488 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Percolation transitions in two dimensions | |
| dc.type | text |