Exchange stiffness of a spin-glass

Numerical estimates are reported for the exchange-stiffness constant ρₛ of a dilute, Ruderman-Kittel-Kasuya-Yosida---coupled spin-glass at zero temperature. Conventional stiffness behavior is found, with no resolved trend in ρₛ over simulation volumes of constant cross section and lengths in the ratio 1:2:3. The value of ρₛ is found to scale as c4/3 (c being the atomic fraction of magnetic ions), as expected for an r^-3 interaction potential and to be {~}25 times smaller than the value for a comparable ferromagnet. When one uses the Halperin-Saslow expression for the spin-wave dispersion constant, a parabolic density of spin-wave modes is found which is consistent with the low-frequency (ω0.2 meV) density of excitations recently given for 0.9 at.% Mn in Cu from numerical simulation studies.