Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the Edwards-Anderson Ising Model on Complex Networks
Chiaki Yamaguchi
TL;DR
This paper analytically determines the percolation thresholds of Fortuin-Kasteleyn clusters in the Edwards-Anderson Ising model on complex networks, covering various models and including Nishimori line results.
Contribution
It provides a unified analytical framework for percolation thresholds across different Edwards-Anderson Ising models on arbitrary degree distribution networks.
Findings
Percolation thresholds derived for Nishimori line
Results extended to ±J, diluted ±J, and Gaussian models
Thresholds obtained for infinite-range and SK models
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 model and the Sherrington-Kirkpatrick model are also shown.
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