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

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

2007-12-20

arxiv.org/abs/0712.3540v1

Phys. Rev. E 77, 061139 (2008)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures

Scientific paper

10.1103/PhysRevE.77.061139

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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