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

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  • Cengiz, Tunç
  • Albayrak, Erhan

Abstract

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.

Suggested Citation

  • Cengiz, Tunç & Albayrak, Erhan, 2012. "The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(10), pages 2948-2956.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:10:p:2948-2956
    DOI: 10.1016/j.physa.2012.01.032
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