Square lattice site percolation at increasing ranges of neighbor interactions
| dc.creator | Malarz, K. | |
| dc.creator | Galam, S. | |
| dc.date | 2004-08-15 | |
| dc.date.accessioned | 2026-07-07T02:59:46Z | |
| dc.date.available | 2026-07-07T02:59:46Z | |
| dc.description | We report site percolation thresholds for square lattice with neighbor interactions at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (N$^2$), next nearest neighbors (N$^3$), next next nearest neighbors (N$^4$) and fifth nearest neighbors (N$^6$) yield the same $p_c=0.592...$. At odds, fourth nearest neighbors (N$^5$) give $p_c=0.298...$. These results are given an explanation in terms of symmetry arguments. We then consider combinations of various ranges of interactions with (N$^2$+N$^3$), (N$^2$+N$^4$), (N$^2$+N$^3$+N$^4$) and (N$^2$+N$^5$). The calculated associated thresholds are respectively $p_c=0.407..., 0.337..., 0.288..., 0.234...$. The existing Galam--Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices. | |
| dc.description | 4 pages, revtex4 | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0408338 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0408338 | |
| dc.identifier | Phys. Rev. E71 (2005) 016125 | |
| dc.identifier | doi:10.1103/PhysRevE.71.016125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24641 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Square lattice site percolation at increasing ranges of neighbor interactions | |
| dc.type | text |