Griffiths-McCoy singularities, Lee-Yang zeros, and the cavity method in a solvable diluted ferromagnet.
We study the diluted Ising ferromagnet on the Bethe lattice as a case study for the application of the cavity method to problems with Griffiths-McCoy singularities. Specifically, we are able to make much progress at infinite coupling where we compute, from the cavity method, the density of Lee-Yang zeros in the paramagnetic Griffiths region as well as the properties of the phase transition to the ferromagnet. This phase transition is itself of a Griffiths-McCoy character albeit with a power law distribution of cluster sizes.
Laumann
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Department of Physics, Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA.
Scardicchio
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Sondhi
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