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

  title={The weak limit of Ising models on locally tree-like graphs},
  author={Andrea Montanari and Elchanan Mossel and Allan Sly},
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weak 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 Gn are expanders we derive a more detailed understanding by showing convergence of the Ising… CONTINUE READING
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