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

Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field

“…The theoretical treatment of the sound propagation by mode-mode coupling method predicts that the sound attenuation coefficient scales as ∼ for the sound frequencies that are quite larger than the characteristic frequency of the order parameter fluctuations and an extensive study of the frequency dispersion of the critical attenuation of KMnF 3 above 186.2 K measured = 0.13 ± 0.05 [53][54][55]. In addition, similar frequency dependence of the sound attenuation coefficient has been reported for various model systems such as spin-1 and spin-3/2 Ising models on the Bethe lattice [39,40], zero crystal field BEG model [37], and metamagnetic Ising model [38] within mean-field theory.…”

“…Further, the temperature at which attenuation maxima take place moves to lower temperatures with rising frequency. The frequency shift of the attenuation maxima is also observed in the experimental and theoretical studies of the ultrasonic investigation of liquid helium [56,57] and Rb 2 ZnCl 4 and K 2 SeO 4 [58] as well as other Ising models [37][38][39][40] and elastically isotropic Ising system above the critical point on the basis of a complete stochastic model [59].…”

“…The attenuation peak broadens and its amplitude decreases and shifts to lower temperatures with decreasing , while = 0.2. We should note that, for systems that have two or more order parameters, the relation between the generalized forces and currents may be written in terms of a matrix of phenomenological rate coefficients and the effect of the nondiagonal Onsager coefficient has been investigated for BEG and metamagnetic Ising models in the mean-field approximation [37,38] and spin-3/2 and spin-1 Ising models on the Bethe lattice [39,40]. The critical behavior of the sound attenuation coefficient in the neighborhood of the second-order phase transition points is characterized by the dynamical sound attenuation critical exponent .…”

“…Gulpinar investigated the critical behavior of ultrasound wave absorption coefficient in the metamagnetic Ising model within the mean-field approximation [38]. Later, the absorption of sound in the spin-3/2 Ising model on the Bethe lattice is obtained and its temperature variance is analyzed near the phase transition points [39]. Recently, Cengiz and Albayrak studied the sound attenuation phenomena for a finite crystal field BEG model on the Bethe lattice in terms of the recursion relations by using the Onsager theory [40].…”

Effective-field theory on the kinetic spin-3/2 Ising model

“…Keskin et al investigated the dynamic phase diagram of spin-3/2 Ising model under an oscillating magnetic field by the use of the mean-field theory (MFT) [23][24][25][26]. Cengiz et al studied the ultrasonic attenuation on the Bethe lattice for a spin-3/2 Ising model using the Onsager theory of irreversible thermodynamics [27]. Vatansever et al investigated the relaxation and complex magnetic susceptibility treatments of a spin-3/2 Ising model by a method combining the statistical equilibrium theory and the thermodynamics limit [28].…”