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

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.

11 pages, 7 figures

References in corpus (7)

• The Bethe lattice spin glass revisited
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Quantum Belief Propagation
• Griffith Singularities and the Replica Instantons in the Random Ferromagnet
• Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
• Griffiths singularities in the two dimensional diluted Ising model
• Griffiths singularity in the random Ising ferromagnet

Cited by in corpus (4)

• Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet
• Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice
• Subdiffusive spin transport in disordered classical Heisenberg chains
• Multi-step relaxations in Glauber dynamics of a bond-diluted Ising model on a Bethe lattice