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Spin-1 Ising model on tetrahedron recursive lattices: Exact results

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  • Jurčišinová, E.
  • Jurčišin, M.

Abstract

We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z=6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.

Suggested Citation

  • Jurčišinová, E. & Jurčišin, M., 2016. "Spin-1 Ising model on tetrahedron recursive lattices: Exact results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 554-568.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:554-568
    DOI: 10.1016/j.physa.2016.06.049
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    1. Ananikian, N.S. & Izmailian, N.Sh. & Oganessyan, K.A., 1998. "An Ising spin-S model on generalized recursive lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 207-214.
    2. Chakraborty, K.G. & Tucker, J.W., 1986. "Statistical mechanics of a spin-one Ising model on a Bethe lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 137(1), pages 122-136.
    3. 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.
    4. Kaneyoshi, T., 2000. "Decoupling approximation in spin-S(S≧1/2) Ising systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(3), pages 518-530.
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