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

TL;DR

This paper analytically determines the percolation thresholds of Fortuin-Kasteleyn clusters in a Potts gauge glass model on complex networks, linking percolation and dynamical transitions along the Nishimori line.

Contribution

It provides the first analytical results for percolation thresholds of FK clusters in a Potts gauge glass model on complex networks, extending previous models.

Findings

Percolation thresholds derived analytically on the Nishimori line

Results applicable to random graphs with arbitrary degree distributions

Includes analysis of the infinite-range model

Abstract

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