Crossing probabilities on same-spin clusters in the two-dimensional Ising model
| dc.creator | Lapalme, Ervig | |
| dc.creator | Saint-Aubin, Yvan | |
| dc.date | 2000-05-11 | |
| dc.date.accessioned | 2026-07-07T10:53:22Z | |
| dc.date.available | 2026-07-07T10:53:22Z | |
| dc.description | Probabilities of crossing on same-spin clusters, seen as order parameters, have been introduced recently for the critical 2d Ising model by Langlands, Lewis and Saint-Aubin. We extend Cardy's ideas, introduced for percolation, to obtain an ordinary differential equation of order 6 for the horizontal crossing probability pih. Due to the identity pih(r)+pih(1/r)=1, the function pih must lie in a 3-dimensional subspace. New measurements of pih are made for 40 values of the aspect ratio r (r in [0.1443,6.928]). These data are more precise than those obtained by Langlands et al as the 95%-confidence interval is brought to 4x10^{-4}. A 3-parameter fit using these new data determines the solution of the differential equation. The largest gap between this solution and the 40 data is smaller than 4x10^{-4}. The probability pihv of simultaneous horizontal and vertical crossings is also treated. | |
| dc.description | 13 pages, 2 figures, latex | |
| dc.identifier | https://arxiv.org/abs/hep-th/0005104 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0005104 | |
| dc.identifier | J.Phys.A34:1825-1836,2001 | |
| dc.identifier | doi:10.1088/0305-4470/34/9/302 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/185459 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Crossing probabilities on same-spin clusters in the two-dimensional Ising model | |
| dc.type | text |