acoustic signatures of the phases and phase transitions in the blume capel model with random crystal field

Sound propagation in the Blume Capel model with quenched diluted single-ion anisotropy is investigated. The sound dispersion relation and an expression for the ultrasonic attenuation are derived with the aid of the method of thermodynamics of irreversible processes. A frequency-dependent dispersion minimum that is shifted to lower temperatures with rising frequency is observed in the ordered region. The thermal and sound frequency (ω) dependencies of the sound attenuation and effect of the Onsager rate coefficient are studied in low- and high-frequency regimes. The results showed that ωτ≪1 and ωτ≫1 are the conditions that describe low- and high-frequency regimes, where τ is the single relaxation time diverging in the vicinity of the critical temperature. In addition, assuming a linear coupling of sound wave with the order parameter fluctuations in the system and ε as the temperature distance from the critical point, we found that the sound attenuation follows the power laws α(ω,ε)~ω2ε-1 and α(ω,ε)~ω0ε1 in the low- and high-frequency regions, while ε→0. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is presented and it is shown that a good agreement is found with our results.