Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the Edwards-Anderson Ising Model on Complex Networks

Abstract

We analytically show the percolation thresholds of the Fortuin-Kasteleyn cluster for the Edwards-Anderson Ising model on random graphs with arbitrary degree distributions. The results on the Nishimori line are shown. We obtain the results for the +-J model, the diluted +-J model, and the Gaussian model, by applying an extension of a criterion for the random graphs with arbitrary degree distributions. The results for the infinite-range $\pm J$ model and the Sherrington-Kirkpatrick model are also shown.

16 pages, 4 figures. v4: minor corrections/additions

References in corpus (1)

• The structure and function of complex networks

Cited by in corpus (4)

• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model