The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature ( T ), frequency ( w ), Onsager coefficient ( γ ) and external magnetic field ( H ) near the second-order ( T c ) and first-order ( T t ) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient ( α ) . Our investigations revealed that only one peak is obtained near T t and three peaks are found near T c when the Onsager coefficient is varied at a given constant frequency for q = 3 . Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q = 3 , 4 and 6 near T c . The sound attenuation peaks are observed near T t at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.