Conjectured exact percolation thresholds of the Fortuin–Kasteleyn cluster for the ±J Ising spin glass model

Abstract

The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster for the ±J Ising spin glass model are theoretically shown based on a conjecture. It is pointed out that the percolation transition of the Fortuin-Kasteleyn cluster for the spin glass model is related to a dynamical transition for the freezing of spins. The present results are obtained as locations of points on the so-called Nishimori line, which is a special line in the phase diagram. We obtain