Stiffness of the Ground-State of a Heisenberg Spin-Glass Model

We examine the stiffness of the ground-state of the Heisenberg spin-glass (SG) model in two ( d = 2) and three ( d = 3) dimensions. We calculate the excess energy Δ E L (ω) which is gained by twisting the system of size L d -1 ×( L +1) by a twist angle ω. We find that the energy can be scaled as Δ E L (ω) ∼ A ω α L θ s with α∼1.9, and θ s ∼0 for d = 2 and θ s ∼0.8 for d = 3. These results are significantly different from those of the conventional defect energy method but rather similar to those of the pure ferromagnetic Heisenberg model. Thus, it is suggested that, in d = 3, the SG phase might occur at finite temperatures.