CRITICAL BEHAVIORS OF THE SOUND ATTENUATION IN A SPIN-1 ISING MODEL
Rıza Erdem1 and Mustafa Keskin2
1Department of Physics, Gaziosmanpaşa
University, 60110 Tokat, Turkey
2Department of Physics, Erciyes
University, 38039 Kayseri, Turkey
of the sound attenuation in a spin-1 Ising system with bilinear and
biquadratic interactions  are investigated within the framework of
Onsager theory of irreversible thermodynamics . The sound-wave is
assumed to couple mainly to the order parameter fluctuations which decay
via order parameter relaxation processes. Two relaxation times are
obtained and an expression is found for the sound attenuation coefficient
(a) in terms of these
relaxation times. The temperature behavior of the sound attenuation is
anayzed according to various values of Onsager or phenomenological rate
coefficients (Lij). For all LS
and LQ values it is observed
that the sound attenuation peaks occur below the phase transition points
and depend on both frequency (w)
and off-diagonal Onsager coefficient (L).
On the other hand, a convergence is found in attenuation just below the
critical and the tricritical points as (Tc-T),
while a jump-discontinuity is observed for the first-order behavior.
Moreover, the frequency variation of the sound attenuation is also
investigated and w2-attenuation dependence is observed in the hydrodynamic regime. These
results are in a good agreement with ultrasonic investigations of some
magnetic systems, such as MnF2, FeF2,
and RbMnF3 .
| M. Keskin and R. Erdem,
J. Stat. Phys, 89, 1035 (1997); R. Erdem and M. Keskin, phys. stat. sol.
(b) 225, 145 (2001); Phys. Rev. E 64, 026102 (2001); Phys. Lett. A 291,
| L. Onsager, Phys. Rev.
37, 405 (1931); 38, 2265 (1931); S. R. de Groot, Thermodynamics of
Irreversible Processes (North-Holland Publishing Company, Amsterdam,
1951); S.R. de Groot and P. Mazur, Non- equilibrium Thermodynamics (North-Holland,
| T. J.
Moran and B. Lüthi, Phys. Rev. B4, 122 (1971); A. Ikushima and R.
Feigelson, J. Phys. Chem. Solids 32, 417 (1971); T. Jimbo and C. Elbaum,
Phys. Rev. Lett. 28, 1393 (1972); A. Bachellerie, J. Joffrin and A.
Levelut, Phys. Rev. Lett. 30, 617 (1973).