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Differential operator technique for higher spin problems

Author

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  • Kaneyoshi, T.
  • Tucker, J.W.
  • Jaščur, M.

Abstract

A new effective-field theory for the Blume-Capel model with a high spin value S is developed by making use of exact spin identities and taking advantage of the differential operator technique. The general formulation for evaluating the transition line and the tricritical point is derived. In particular, the phase diagrams are examined for S = 32 and S = 2. Our results show that the tricritical behavior does not exist in the spin-32 Blume-Capel model but does exist in the spin-2 Blume-Capel model. The tricritical point in the S = 2 system is found at D/zJ≅−0.498, where z is the coordination number, D the crystal-field constant and J the exchange interaction.

Suggested Citation

  • Kaneyoshi, T. & Tucker, J.W. & Jaščur, M., 1992. "Differential operator technique for higher spin problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(3), pages 495-512.
    • Handle: RePEc:eee:phsmap:v:186:y:1992:i:3:p:495-512
    DOI: 10.1016/0378-4371(92)90212-9
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    References listed on IDEAS

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    1. Tanaka, Yoshiaki & Uryû, Norikiyo, 1981. "Magnetic specific heat of the honeycomb lattice of spin one-half with anisotropic Heisenberg exchange by a new method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(3), pages 629-637.
    2. Siqueira, A.F. & Fittipaldi, I.P., 1986. "New effective-field theory for the Blume-Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(3), pages 592-611.
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    Cited by:

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    5. Si, Nan & Su, Xin & Meng, Jing & Miao, Hai-Ling & Zhang, Yan-Li & Jiang, Wei, 2020. "Magnetic properties of decorated 2D kagome-like lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
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    7. Schmidt, M. & Dias, P.F., 2021. "Correlated cluster mean-field theory for Ising-like spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    8. Huang, Jinhua & Shi, Xiaoling & Song, Zhaoyuan & Shi, Yingguo, 2017. "Dynamic critical temperature in MnIIFeIII bimetallic oxalates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 460-466.
    9. Silva, Joeliton B. & de Albuquerque, Douglas F., 2022. "Tricritical behavior of the spin-3/2 anisotropic Heisenberg model with Dzyaloshinskii–Moriya interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    10. Lu, Zhao-Ming & Si, Nan & Wang, Ya-Ning & Zhang, Fan & Meng, Jing & Miao, Hai-Ling & Jiang, Wei, 2019. "Unique magnetism in different sizes of center decorated tetragonal nanoparticles with the anisotropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 438-456.

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