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Application of the Monte Carlo method for evaluating the Niemeijer-van Leeuwen cumulant expansion

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Zeitschrift für Physik B Condensed Matter

Abstract

We show that the large cell size problem of the real space renormalization can be handled effectively by Monte Carlo methods. As a demonstration, the second-order cumulant expansion is calculated for the three-dimensional simple cubic Ising model, using a 3 × 3 × 3 cell.

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References

  1. Wilson, K.G., Kogut, J.: Phys. Rep.12 C, 76 (1974)

    Google Scholar 

  2. Niemeijer, Th., van Leeuwen, J.M.J.: Phys. Rev. Lett.31, 1411 1973; Physica (Utr.)71, 17 (1974)

    Google Scholar 

  3. Kadanoff, L.P.: Phys. Rev. Lett.34, 1005 (1975)

    Google Scholar 

  4. Migdal, A.A.: Zh. ETF69, 1457 (1975)

    Google Scholar 

  5. Ma, S.: Phys. Rev. Lett.37, 461 (1976)

    Google Scholar 

  6. Hsu, S., Niemeijer, Th., Gunton, J.D.: Phys. Rev. B11, 2699 (1975)

    Google Scholar 

  7. Sudbø, A.S., Hemmer, P.C.: Phys. Rev. B13, 980 (1976)

    Google Scholar 

  8. Harris, A.B., Lubensky, T.C.: Phys. Rev. Lett.33, 1540 (1974)

    Google Scholar 

  9. Tatsumi, T., Kawasaki, K.: Prog. Theor. Phys.55, 612 (1976)

    Google Scholar 

  10. Hilhorse, H.J.: Phys. Lett. A56, 153 (1976)

    Google Scholar 

  11. Lublin, D.M.: Phys. Rev. Lett.34, 568 (1975)

    Google Scholar 

  12. Rogiers, J., Dekeyser, R.: Phys. Rev. B13, 4886 (1976)

    Google Scholar 

  13. Fields, J.N., Fogel, M.B.: Physica A80, 411 (1975)

    Google Scholar 

  14. Hsu, S., Gunton, J.D.: Phys. Rev. B15, 2688 (1977)

    Google Scholar 

  15. Hemmer, P.C., Velarde, M.G.: J. Phys. A9, 1713 (1976)

    Google Scholar 

  16. Jan, N., Glazer, A.M.: Phys. Lett. A59, 3 (1976)

    Google Scholar 

  17. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: J. Chem. Phys.21, 1087 (1953)

    Google Scholar 

  18. Binder, K.: In: Phase Transitions and Critical Phenomena, Vol. 5 B. p. 2 (edited by C. Domb and M.S. Green) New York: Academic, 1976

    Google Scholar 

  19. Kadanoff, L.P.: Physics2, 263 (1966)

    Google Scholar 

  20. Hsu, S.: Ph. D. dissertation (Temple University, 1976) unpublished

  21. Glauber, R.: J. Math. Phys. N.Y.4, 234 (1963)

    Google Scholar 

  22. See e.g. Kadanoff, L.P., Houghton, A., Yalabik, M.C.: J. Stat. Phys.14, 171 (1976)

    Google Scholar 

  23. Müller-Krumbhaar, H., Binder, K.: J. Stat. Phys.8, 1 (1973)

    Google Scholar 

  24. Peretto, P.: Solid State Comm.19, 235 (1976)

    Google Scholar 

  25. Domb, C.: In: Phase Transitions and Critical Phenomena, Vol. 3, ed. by C. Domb and M.S. Green, London, Academic Press

  26. Nienhuis, B., Nauenberg, M.: Phys. Rev. Lett.35, 477 (1975)

    Google Scholar 

  27. Friedman, Z., Felsteiner, J.: Phys. Rev. B15, 5317 (1977)

    Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, Eötvös University, Budapest, Hungary

    Z. Rácz & P. Ruján

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  1. Z. Rácz
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  2. P. Ruján
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Rácz, Z., Ruján, P. Application of the Monte Carlo method for evaluating the Niemeijer-van Leeuwen cumulant expansion. Z Physik B 28, 287–290 (1977). https://doi.org/10.1007/BF01317255

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  • DOI: https://doi.org/10.1007/BF01317255

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