Journal of Statistical Physics

, Volume 73, Issue 3–4, pp 775–788 | Cite as

The van Hemmen spin glass revisited

  • T. Celik
  • U. H. E. Hansmann
  • M. Katoot
Short Communications

Abstract

We simulated the van Hemmen spin glass model by multicanonical algorithm. The exact results for this mean-field model are reproduced. Physical quantities such as energy density, specific heat, susceptibility and order parameters are evaluated at all temperatures. We also studied an alternate model with short range interactions, which displays the many-valley picture in 2D for random variables having values ±1.

Key words

Monte Carlo multicanonical ensemble spin glasses van Hemmen model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Berg and T. Neuhaus,Phys. Lett. B 267:249 (1991).Google Scholar
  2. 2.
    G. M. Torrie and J. P. Valleau,J. Comput. Phys. 23:187 (1977).Google Scholar
  3. 3.
    B. Berg and T. Neuhaus,Phys. Rev. Lett. 68:9 (1992).Google Scholar
  4. 4.
    B. Berg, U. Hansmann, and T. Neuhaus,Z. Phys. B 90:229 (1993).Google Scholar
  5. 5.
    W. Janke, B. Berg, and M. Katoot,Nucl. Phys. B 382:649 (1992).Google Scholar
  6. 6.
    B. Berg, U. Hansmann, and T. Neuhaus,Phs. Rev. B 47:497 (1993).Google Scholar
  7. 7.
    B. Berg and T. Celik,Phys. Rev. Lett. 69:2292 (1992).Google Scholar
  8. 8.
    B. Berg and T. Celik,Int. J. Mod. Phys. C 3:125 (1992).Google Scholar
  9. 9.
    B. Berg, T. Celik, and U. Hansmann,Europhys. Lett. 22:63 (1993).Google Scholar
  10. 10.
    E. Marinari and G. Parisi,Europhys. Lett. 19:451 (1992).Google Scholar
  11. 11.
    U. Hansmann and Y. Okamoto, FSU-SCRI-93-12;J. Comp. Chem., submitted.Google Scholar
  12. 12.
    S. Kirkpatrick, C. P. Gelatt, and M. P. Vecchi,Science 220:671 (1983).Google Scholar
  13. 13.
    J. L. van Hemmen,Phys. Rev. Lett. 49:409 (1982); A. C. D. van Enter and J. L. van Hemmen,Phys. Rev. A 29:355 (1984); J. L. Van Hemmen, A. C. D. van Enter, and J. Canisius,Z. Phys. B 50:311 (1983).Google Scholar
  14. 14.
    D. Sherrington and S. Kirkpatrick,Phys. Rev. Lett. 35:1792 (1975);Phys. Rev. B 12:4384 (1978).Google Scholar
  15. 15.
    K. Binder and A. P. Young,Rev. Mod. Phys. 58:801 (1986).Google Scholar
  16. 16.
    K. Binder and K. Schroder,Phys. Rev. B 14:2142 (1976).Google Scholar
  17. 17.
    M. A. Ruderman and C. Kittel,Phys. Rev. 96:99 (1954); T. Kasuya,Prog. Theor. Phys. 16:45 (1956); K. Yosida,Phys. Rev. 106:893 (1957).Google Scholar
  18. 18.
    D. C. Mattis,Phys. Lett. 56:421 (1976).Google Scholar
  19. 19.
    R. N. Bhatt and A. P. Young,Phys. Rev. B 37:5606 (1988).Google Scholar
  20. 20.
    I. Moregenstern and J. L. van Hemmen,Phys. Rev. B 32:6058 (1985).Google Scholar
  21. 21.
    R. B. Griffiths, C.-Y. Weng, and J. S. Langer,Phys. Rev. 149:301 (1966).Google Scholar
  22. 22.
    Ph. de Smedt, J. O. Indekeu, and L. Zhang,Physica A 140: 450 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • T. Celik
    • 1
  • U. H. E. Hansmann
    • 2
  • M. Katoot
    • 3
  1. 1.Supercomputer Computations Research Institute (SCRI)Florida State UniversityTallahasseeUSA
  2. 2.Department of PhysicsFlorida State UniversityTallahasseeUSA
  3. 3.Department of Physical SciencesEmbry-Riddle Aeronautical University (ERAU)Daytona BeachUSA

Personalised recommendations