|
Hokkaido University Collection of Scholarly and Academic Papers >
Creative Research Institution >
Peer-reviewed Journal Articles, etc >
Lace Expansion for the Ising Model
| Title: | Lace Expansion for the Ising Model |
| Authors: | Sakai, Akira Browse this author →KAKEN DB |
| Issue Date: | 2007 |
| Publisher: | Springer |
| Journal Title: | Communications in Mathematical Physics |
| Volume: | 272 |
| Issue: | 2 |
| Start Page: | 283 |
| End Page: | 344 |
| Publisher DOI: | 10.1007/s00220-007-0227-1 |
| Abstract: | 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 twopoint 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. |
| Rights: | "The original publication is available at www.springerlink.com" |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/44914 |
| Appears in Collections: | 創成研究機構 (Creative Research Institution) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 坂井 哲
|
