# The Ising model and percolation on trees and tree-like graphs

@article{Lyons1989TheIM, title={The Ising model and percolation on trees and tree-like graphs}, author={Russell Lyons}, journal={Communications in Mathematical Physics}, year={1989}, volume={125}, pages={337-353} }

We calculate the exact temperature of phase transition for the Ising model on an arbitrary infinite tree with arbitrary interaction strengths and no external field. In the same setting, we calculate the critical temperature for spin percolation. The same problems are solved for the diluted models and for more general random interaction strengths. In the case of no interaction, we generalize to percolation on certain tree-like graphs. This last calculation supports a general conjecture on the…

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