|
|||||
|
|
Universality in the 2D Ising model and conformal invariance of fermionic observables |
|
| Authors: | Dmitry Chelkak Stanislav Smirnov |
| Affiliation: | 1. St.Petersburg Department of Steklov Mathematical Institute (PDMI RAS), Fontanka 27, 191023, St. Petersburg, Russia 3. Chebyshev Laboratory, Department of Mathematics and Mechanics, Saint-Petersburg State University, 14th Line, 29b, 199178, Saint-Petersburg, Russia 2. Section de Math??matiques, Universit?? de Gen??ve, 2-4 rue du Li??vre, Case postale 64, 1211, Gen??ve 4, Switzerland |
| Abstract: | It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof has ever been given, and even physics arguments support (a priori weaker) M?bius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |