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 zeros 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.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - Jun 27 2008
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability