Sensitivity to changes in boundary conditions in S = 1 Ising spin glasses

Transfer-matrix-based calculations of the defect energy in two-dimensional S = 1 Ising spin glasses yield a T = 0 exponent y which depends on the state of the spins at the boundary walls. If the boundary spins are not allowed to be in the zero state, the exponent y agrees with the value obtained for S = 12. Otherwise the exponent is different and S-dependent. We argue that the lower critical dimensionality should not depend on S. Our results point out the importance of selecting boundary conditions that capture the physics of the problem.