The weak limit of Ising models on locally tree-like graphs

Andrea Montanari, Elchanan Mossel, Allan Sly

Research output: Contribution to journalArticle

19 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)31-51
Number of pages21
JournalProbability Theory and Related Fields
Volume152
Issue number1-2
DOIs
StatePublished - Feb 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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