Propagation of Sound in a Spin-Glass

Sound propagation and damping are studied near the spin-glass transition for a time-dependent Landau-Ginzburg model coupled to phonons. The sound speed decreases linearly with $T-T_g$, and the sound damping diverges as ${(T-T_g)}^{-1\mathrm{}}$, when the spin-glass transition, $T_g$, is approached from high temperatures. At the spin-glass transition, the sound speed has a term proportional to ${\omega }^{\frac{1}{2}}$, and the sound damping is proportional to ${\omega }^{-\frac{1}{2}}$.