Spin-lattice relaxation effects in critical sound propagation

The nonasymptotic critical properties of sound propagation are studied in compressible Ising system above T-C. In the present paper we analyse a model where in addition to the coupling to two order-parameter fluctuations the sound mode couples linearly to the fluctuations of spin-energy an lattice-energy densities. Both subsystems exchange energy with the rate determined by the bare spin-lattice relaxation time. The total energy may be conserved or not. The crossover between insulator-like behaviour similar to t(-2 alpha) and metal-like behaviour similar to t(-(z nu+alpha)) in ultrasonic attenuation is investigated according to the value of ultrasonic frequency, the reduced temperature t, bare relaxation times and various coupling constants.