Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet

C. Laumann; A. Scardicchio; S. L. Sondhi

doi:10.1103/physreve.77.061139

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arXiv · 0712.3540

Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet

C. Laumann·A. Scardicchio·S. L. Sondhi

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Abstract

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 zeroes 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.

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C. Laumann, A. Scardicchio, S. L. Sondhi. 2007-12-20. Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet. https://doi.org/10.1103/physreve.77.061139

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