Montanari, AndreaMossel, ElchananSly, Allan2023-05-232023-05-232012-02-012016-07-12https://repository.upenn.edu/handle/20.500.14332/47923We 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.The final publication is available at Springer via http://dx.doi.org/[10.1007/s00440-010-0315-6.Statistics and ProbabilityArticle