Ground-state behavior of the three-dimensional ±J random-bond Ising model

Large numbers of ground states of the three-dimensional ±J random-bond Ising model are calculated for sizes up to 14³ using a combination of a genetic algorithm and cluster-exact approximation. Several quantities are calculated as functions of the concentration p of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of pc=0.222±0.005 is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents {ν}=1.1±{}0.3 and {β}=0.2±{}0.1 are calculated. The behavior of the distribution of overlaps $P(q)$ is used to investigate how the spin-glass phase evolves with increasing concentration $p.$ The spin-glass order is characterized by a broad distribution of overlaps which extends down to $q=0.$