2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164674We 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 figuresStatistical MechanicsDisordered Systems and Neural Networkstext