Advertisement

Monte Carlo Simulations of Three-Dimensional Heisenberg and Transverse-Ising Magnets

  • O. Nagai
  • Y. Yamada
  • Y. Miyatake
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 74)

Abstract

The three-dimensional quantum magnets are studied by use of the Monte Carlo method based on Suzuki’s theory. In the calculation for a Heisenberg model, we adopted Cullen and Landau’s algorithms. We find that the Monte Carlo result for a simple cubic ferromagnet is in reasonable agreement with the previous result. Also, the Monte Carlo simulations for a transverse-Ising magnet are performed by using a multispin flip or spin cluster flip method. The computed results for a ferromagnetic transverse-Ising model are satisfactory. In the case of the antiferromagnetic triangular lattice, a phasetransition-like behavior is observed at a finite value of the transverse field.

Keywords

Monte Carlo Monte Carlo Simulation Heisenberg Model Transverse Field Dimensional Lattice 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. C. Mattis: The Theory of Magnetism I and II, Springer Ser. Solid-State Sci., Vol.17 and Vol.55 (Springer, Berlin, Heidelberg 1981 and 1985 )Google Scholar
  2. 2.
    K. Binder: In Monte Carlo Methods in Statistical Physics ed. by K. Binder, (Springer, Berlin, Heidelberg 1979 ) p. 1Google Scholar
  3. 3.
    M. Suzuki: Prog. Theor. Phys. 56, 1454 (1976)ADSzbMATHCrossRefGoogle Scholar
  4. 4.
    M. Suzuki, S. Miyashita, and AT-Kuroda: Prog. Theor. Phys. 58, 701 (1977)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    H. F. Trotter: Proc. Am. Math. Soc. 10, 545 (1950)MathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Suzuki: J. Stat. Phys. 43, 883 (1986)ADSCrossRefGoogle Scholar
  7. 7.
    H. De Raedt and A. Lagendijk: Phys. Rep. 127, 233 (1985)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    J. C. Bonner and M. E. Fisher: Phys. Rev. A135, 640 (1964)ADSCrossRefGoogle Scholar
  9. 9.
    J. J. Cullen and D. P. Landau: Phys. Rev. B27, 297 (1983)ADSCrossRefGoogle Scholar
  10. 10.
    G. S. Rushbrooke, G. A. Baker, Jr. and P. J. Wood: Phase Transitions and Critical Phenomena: eds. C. Domb and M. S. Green, Vol.3 ( Academic Press, New York, 1972 ) p. 246Google Scholar
  11. 11.
    S. Katsura: Phys. Rev. 127, 1508 (1962)ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    E. Lieb, T. Schultz and D. Mattis: Ann. Phys. 16, 407 (1961)MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    M. E. Fisher: Physica (Utrecht) 26, 613 (1960)ADSCrossRefGoogle Scholar
  14. 14.
    P. Pfeuty: Ann. Phys. (NY): 57, 79 (1962)ADSCrossRefGoogle Scholar
  15. 15.
    M. Suzuki: Phys. Lett. 34A, 94 (1971)CrossRefGoogle Scholar
  16. 16.
    A. Wiesler: Phys. Lett. 89A, 359 (1982)CrossRefGoogle Scholar
  17. 17.
    Y. Miyatake, Y. Yamada, K. Nishino, M. Toyonaga, and O. Nagai: J. Mag. Mag. Mat. 54–57, 687 (1986)Google Scholar
  18. 18.
    R. J. Elliott and C. Wood: J. Phys. C: Solid St. Phys. 4, 2359 (1971)ADSCrossRefGoogle Scholar
  19. 19.
    P. Pfeuty and R. J. Elliott: J. Phys. C: Solid St. Phys. 4, 2370 (1971)ADSCrossRefGoogle Scholar
  20. 20.
    M. Barma and B. S. Shastry: Phys. Rev. B18, 3351 (1978)ADSCrossRefGoogle Scholar
  21. 21.
    M. Suzuki: Phys. Lett. Alll 299 (1985)Google Scholar
  22. 22.
    C. Rebbi: In The Applications of Monte Carlo Methods in Statistical Physics ed. by K. Binder ( Springer, Berlin Heidelberg 1984 ) p. 277Google Scholar
  23. 23.
    C. Kalle and V. Winkelman: J. Stat. Phys. 28, 639 (1982)ADSCrossRefGoogle Scholar
  24. 24.
    M. Suzuki, S. Miyashita, and A. Kuroda: Prog. Theor. Phys. 58, 1377 (1977)ADSzbMATHCrossRefGoogle Scholar
  25. 25.
    S. Miyashita: Prog. Theor. Phys. 63, 797 (1980)ADSCrossRefGoogle Scholar
  26. 26.
    Y. Miyatake, M. Yamamoto, J. J. Kim, M. Toyonaga, and O. Nagai: J. Phys. C: Solid St. Phys. 19, 2539 (1986)ADSCrossRefGoogle Scholar
  27. 27.
    O. Nagai, Y. Miyatake, Y. Yamada, and H. T. Diep: J. Mag. Mag. Mat. 54–57, 681 (1986)Google Scholar
  28. 28.
    J. Oitmaa and G. J. Coomb: J. Phys. C: Solid St. Phys. 14, 143 (1981)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • O. Nagai
    • 1
  • Y. Yamada
    • 1
  • Y. Miyatake
    • 1
  1. 1.Department of Physics,Faculty of ScienceKobe UniversityRokkodai, Kobe 657Japan

Personalised recommendations