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

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

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

Authors

Laumann, C.

Scardicchio, A.

Sondhi, S. L.

Description

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.
11 pages, 7 figures