Ground state of the J Ising spin glass

We study the properties of ground-state configurations of Ising models in which a fraction x of the nearest-neighbor couplings is antiferromagnetic and the rest ferromagnetic, with all couplings of equal magnitude. At T=0, these properties can be understood within the context of zero-energy lines in two dimensions and zero-energy surfaces in three. These define "domain walls" which determine the stability properties of the ground states. We find different types of spin-glass behavior for the square and cubic lattices; the latter may retain a type of long-range magnetic rigidity. Ground-state properties are expected to depend strongly on both the lattice geometry and the choice of coupling distribution.