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

@inproceedings{Montanari2009TheWL,
  title={The weak limit of Ising models on locally tree-like graphs},
  author={Andrea Montanari and Elchanan Mossel and Allan Sly},
  year={2009}
}
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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Montanari , Ising models on locally tree - like graphs

  • A. Dembo, A.
  • Ann . Appl . Prob .
  • 2009

Percolation and number of phases in the two-dimensional Ising model

  • H. O. Georgii, Y. Higuchi
  • J. Math. Phys. 41
  • 2000
1 Excerpt

Phase transitions on nonamenable graphs

  • D. L. Stein
  • J . Math . Phys .
  • 2000

T

  • S. Janson
  • Luczak and A. Ruciński, “Random graphs,” John…
  • 2000

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