CRITICAL BEHAVIORS OF THE SOUND ATTENUATION IN A SPIN1 ISING MODEL

Rıza Erdem^{1 }and Mustafa Keskin^{2}
^{
1Department of Physics, Gaziosmanpaşa
University, 60110 Tokat, Turkey
}
^{
2Department of Physics, Erciyes
University, 38039 Kayseri, Turkey} 
ABSTRACT

Critical behaviors
of the sound attenuation in a spin1 Ising system with bilinear and
biquadratic interactions [1] are investigated within the framework of
Onsager theory of irreversible thermodynamics [2]. The soundwave 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 (L_{ij}). For all L_{S}
and L_{Q} values it is observed
that the sound attenuation peaks occur below the phase transition points
and depend on both frequency (w)
and offdiagonal Onsager coefficient (L).
On the other hand, a convergence is found in attenuation just below the
critical and the tricritical points as (T_{c}T),
while a jumpdiscontinuity is observed for the firstorder behavior.
Moreover, the frequency variation of the sound attenuation is also
investigated and w^{2}attenuation dependence is observed in the hydrodynamic regime. These
results are in a good agreement with ultrasonic investigations of some
magnetic systems, such as MnF_{2}, FeF_{2},
and RbMnF_{3} [3].

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