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

TL;DR

This paper applies the cavity method to a diluted Ising ferromagnet on the Bethe lattice, analyzing Griffiths-McCoy singularities, Lee-Yang zeros, and phase transition properties at infinite coupling.

Contribution

It demonstrates the use of the cavity method to study Griffiths-McCoy singularities and Lee-Yang zeros in a solvable diluted ferromagnet model.

Findings

Computed the density of Lee-Yang zeros in the Griffiths region

Analyzed the phase transition with Griffiths-McCoy characteristics

Identified power-law distribution of cluster sizes at transition

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.