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

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

2009-03-03

arxiv.org/abs/0903.0438v4

Prog. Theor. Phys. 124 (2010), 399-413

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1143/PTP.124.399

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.

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