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In statistical physics, the cavity method can be regarded as a generalization of the Bethe-Peierls iterative method in tree-like graphs to the case of graphs with loops that are not too short. I would like to know whether there is some similar method in statistical physics that can be used to analyze the percolation on graphs with loops that are short, such as square lattices.

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  • $\begingroup$ I think it really depends what you mean by "some similar method". As far as I know the techniques currently used to study percolation on low-dimensional lattices are very different from the cavity method; see e.g. Grimmett's book "Percolation". You may want to update your question to make it more clear what you're asking for. $\endgroup$
    – j.c.
    Oct 16, 2015 at 14:12

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