Monte Carlo Renormalization Group and the Three Dimensional Ising Model

  • Kenneth G. Wilson
Part of the NATO ASI Series book series (NSSB, volume 115)


Precise computations of critical properties of the three dimensional Ising model are available from computations on the ICL DAP (Edinburgh) and the Santa Barbara Ising processor. The computations however are not complete because they do not include reliable information on the correction to scaling exponent. The Monte Carlo Renormalization group is used in the Scottish computations; finite size scaling is used at Santa Barbara. The ideas behind the Monte Carlo Renormalization Group are explained, along with an analysis of the errors involved, to the extent they are presently known.


Ising Model Effective Interaction Monte Carlo Computation Finite Size Effect Monte Carlo Procedure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. S. Pawley, R. H. Swendsen, D. J. Wallace, and K. G. Wilson, Edinburgh preprint 83/238, submitted to Phys. Rev. B.Google Scholar
  2. 2.
    M. N. Barber, R. B. Pearson, D, Toussaint, and J. L. Richardson, Santa Barbara Institute for Theoretical Physics preprint NSF-ITP-83-144.Google Scholar
  3. 3.
    For reviews see T. W. Burkhardt and J. M. J. Van Leeuwen, eds. Real Space Renormalization, (Springer-Verlag, 1982).Google Scholar
  4. 4.
    L. P. Kadanoff, Phys. Rev. Lett, 34, 1005 (1975).ADSCrossRefGoogle Scholar
  5. 5.
    T. L. Bell, and K. G. Wilson, Phys. Rev. B11, 3431 (1975).ADSGoogle Scholar
  6. 6.
    See Refs. 11-13 of Ref. 1.Google Scholar
  7. 7.
    See Ref. 1.Google Scholar
  8. 8.
    F. J. Wegner, in Phase Transitions and Critical Phenomena, C. Domb and M. S. Green, Eds., Vol. VI (Academic Press, 1976) p.34.Google Scholar
  9. 9.
    See Ref. 1.Google Scholar
  10. 10.
    S.-K. Ma, Phys. Rev. Lett. 37, 471 (1976).ADSCrossRefGoogle Scholar
  11. 11.
    K. G. Wilson, Revs. Mod. Phys. 47, 773 (1975).ADSCrossRefGoogle Scholar
  12. 12.
    See, e.g., K. Binder, ed., Monte Carlo Methods in Statistical Physics, Springer, Berlin, 1979.Google Scholar
  13. 13.
    D. Callaway and A. Rahman, Phys. Rev. Lett, 49, 613 (1982); M. Creutz, ibid. 50, 1411 (1983); G. Bhanot, Institute for Advanced Studies preprint.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Kenneth G. Wilson
    • 1
  1. 1.Newman Laboratory of Nuclear StudiesCornell UniversityIthacaUSA

Personalised recommendations