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Fermionization of a Generalized Two-Dimensional Ising Model

  • A. I. Bugrij
Part of the Research Reports in Physics book series (RESREPORTS)

Abstract

The generalized two-dimensional Ising model is a system of spins that interact with partners of two neighboring coordination spheres. In the case of a square lattice the density of the Hamiltonian h(σ R ) (the energy per plaquet) that satisfies the global Z 2-symmetry requirement includes not only pair interactions between first and second neighbors, but also four-spin interactions
$$h\left( {{\sigma _R}} \right) = - \sum\limits_{i < l} {{J_{il}}} \sigma _R^i\sigma _R^l - J\prod\limits_{i = 1}^4 {\sigma _R^i} ,i,l = 1, \ldots ,4.$$
(1)

Keywords

Partition Function Ising Model Pair Interaction Fermion Representation Grassmann Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Onsager L.: Phys.Rev. 65 117–129 (1944)MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Wannier G.H.: Phys.Rev. 79 357–364 (1950)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Baxter R.J.: Phys. Rev. Lett., 26 832–934 (1971)ADSCrossRefGoogle Scholar
  4. 4.
    Wu F.Y.: Phys.Rev. B 4 2312–2314 (1971)Google Scholar
  5. 5.
    Dalton N.W., Wood D.W.:J. Math. Phys. 10 1271–1302 (1969)ADSCrossRefGoogle Scholar
  6. 6.
    Pun C., Wu F.Y.: Phys. Rev. 179 560–570 (1969)ADSCrossRefGoogle Scholar
  7. 7.
    Gibberd R.V.:J. Math. Phys. 10 1026–1029 (1969)Google Scholar
  8. 8.
    Binder K., Landau D.P.: Phys. Rev. B 21 1941–1962 (1980)Google Scholar
  9. 9.
    Bugrij A.I., Schadura V.N.: Physics of Many-Particle Systems, 12 85–95 (1987)Google Scholar
  10. 10.
    Schultz T.D., Mattis D.S., Lied E.H.: Rev. Mod. Phys., 36 856–867 (1964)ADSCrossRefGoogle Scholar
  11. 11.
    Fradkin E.S., Steingradt D.M.: Nuovo Cim. 47 A 115–138 (1978)Google Scholar
  12. 12.
    Bugrij A.I.: Physics of Many-Particle Systems 13 72–80 (1988)Google Scholar
  13. 13.
    Polubarinov I.V.:Preprint JINR, E17-413, 1984, Dubna.Google Scholar
  14. 14.
    Plechko V.N.:Dokl. Akad. Nauk SSSR 281 834–837 (1985)Google Scholar
  15. 15.
    Bugrij A.I.:Preprint ITF-85-114R, 1985, Kiev.Google Scholar
  16. 16.
    Berezin F.A.: Usp. Mat. Nauk 24 3–22 (1969)MathSciNetGoogle Scholar
  17. 17.
    Fradkin E.S. in Problems of Theoretical Physics ( Nauka, Moscow 1969 ) pp. 386–392Google Scholar
  18. 18.
    Plechko V.N.:Teor. Mat. Fiz. 64 150–162 (1985)Google Scholar
  19. 19.
    Vaks V.G., Larkin A.I., Ovchinnikov Yu.N.: J. Teor. Eksper. Fiz. 49 1180–1189 (1965)Google Scholar
  20. 20.
    Landau D.P.:J. Appl. Phys. 42 1284–1285 (1971)Google Scholar
  21. 21.
    Fan C., Wu F.Y.:Phys. Rev. B 2 723–733 (1970)Google Scholar
  22. 22.
    Hantmacher F.R.: Theory of Matrices ( Nauka, Moscow 1966 ) p. 59Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • A. I. Bugrij
    • 1
  1. 1.Institute for Theoretical PhysicsKievUSSR

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