Lace expansion for the Ising model
| dc.creator | Sakai, Akira | |
| dc.date | 2005-10-29 | |
| dc.date | 2006-11-14 | |
| dc.date.accessioned | 2026-07-07T06:47:05Z | |
| dc.date.available | 2026-07-07T06:47:05Z | |
| dc.description | The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we prove the lace expansion for the Ising model that is valid for any spin-spin coupling. For the ferromagnetic case, we also prove that the expansion coefficients obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace-expansion coefficients for self-avoiding walk. As a result, we obtain Gaussian asymptotics of the critical two-point function for the nearest-neighbor model with d>>4 and for the spread-out model with d>4 and L>>1, without assuming reflection positivity. | |
| dc.description | 54 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0510093 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0510093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103546 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 82B27; 82B05 | |
| dc.title | Lace expansion for the Ising model | |
| dc.type | text |