|
|||||
|
|
The weak limit of Ising models on locally tree-like graphs |
|
| Authors: | Andrea Montanari Elchanan Mossel Allan Sly |
| Institution: | 1. Department of Electrical Engineering, Stanford University, Stanford, CA, 94305-9510, USA 2. Department of Statistics, Stanford University, Stanford, CA, 94305-9510, USA 3. Faculty of Mathematics and Computer Science, Weizmann Institute, Rehovot, Israel 4. Departments of Statistics and Computer Science, UC Berkeley, Berkeley, CA, 94720-3860, USA 5. Microsoft Research, Redmond, WA, 98052, USA |
| Abstract: | We consider the Ising model with inverse temperature β and without external field on sequences of graphs G n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the ? boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs G n are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |