Ground-state behavior of the 3d +/-J random-bond Ising model

Large numbers of ground states of the three-dimensional $\pm J$ random-bond Ising model are calculated for sizes up to ${14}^3$ using a combination of a genetic algorithm and Cluster-Exact Approximation. Several quantities are calculated as function 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 $p_c=0.222\pm 0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents $\nu =1.1\pm 0.3$ and $\beta =0.2\pm 0.1$ are calculated.