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It was pointed out by de Arcangelis et al. [Europhys. Lett. 14 (1991), 515]that the correct understanding of the percolation phenomenon of theFortuin-Kasteleyn cluster in the Edwards-Anderson model is important since adynamical transition, which is characterized by a parameter called the Hammingdistance or damage, and the percolation transition are related to a transitionfor a signal propagating between spins. We show analytically the percolationthresholds of the Fortuin-Kasteleyn cluster for a Potts gauge glass model,which is an extended model of the Edwards-Anderson model, on random graphs witharbitary degree distributions. The results are shown on the Nishimori line. Wealso show the results for the infinite-range model.

Percolation Thresholds of the Fortuin-Kasteleyn Cluster for a Potts Gauge Glass Model on Complex Networks: Analytical Results on the Nishimori Line