The Sound Attenuation for the Spin-1 Ising Model on the Bethe Lattice

The temperature ($T$), frequency ($w$), Onsager coefficient ($\gamma$) and external magnetic field ($H$) dependencies of the sound attenuation near the phase transition temperature ($T_{\text{c}}$) is studied for the spin-1 Ising model on the Bethe lattice for given coordination numbers $q$ in terms of the recursion relations by using Onsager theory of irreversible thermodynamics. It was assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process. Two relaxation times are obtained and which are used to find an expression for the sound attenuation coefficient ($\alpha$). It was found that $\alpha$ presents only one peak for all frequencies when $q=6$, and two peaks for $q=3$ and 4 at low frequencies. In addition, $\alpha$ increases with the increasing values of frequency and with the decreasing values of external magnetic field.