The weak limit of Ising models on locally tree-like graphs
成果类型：
Article
署名作者：
Montanari, Andrea; Mossel, Elchanan; Sly, Allan
署名单位：
Stanford University; Stanford University; Weizmann Institute of Science; University of California System; University of California Berkeley; University of California System; University of California Berkeley; Microsoft
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-010-0315-6
发表日期：
2012
页码：
31-51
关键词：
摘要：
We consider the Ising model with inverse temperature beta 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 beta. 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.