A Monte-Carlo Calculation of the Renormalized Coupling Constant for the Three Dimensional Ising Model Using Improved Estimators

  • G. A. BakerJr.
  • N. Kawashima
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 80)


Improved estimators for the second partial of the susceptibility and the correlation length are developed in the context of the Swendsen-Wang algorithm. These estimators have much improved convergence properties. We report Monte Carlo calculations for the renormalized coupling constant for a series of system sizes and temperatures such that the ratio of the correlation length to the system size is about one-tenth. This ratio is small enough so our results can be expected to approximate the thermodynamic limit within a per cent or better. Our results strongly support hyperscaling.


Renormalization Group Correlation Length System Size Thermodynamic Limit Improve Estimator 
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  1. 1.
    K. G. Wilson, Phys. Rev. B 4, 3174, 3184 (1971)ADSMATHCrossRefGoogle Scholar
  2. 2.
    E. Brézin, J.-C. LeGuillou, and J. Zinn-Justin, Phys. Rev. D 15, 1544, 1558 (1977)ADSCrossRefGoogle Scholar
  3. 3.
    G. A. Baker, Jr. Quantitiative Theory of Critical Phenomena, ( Academic Press, Boston, 1990 )Google Scholar
  4. 4.
    P. Tamayo, and R. Gupta, private communication. We wish to thank these authors for permission to cite this result in advance of publication.Google Scholar
  5. 5.
    G. A. Baker, Jr. and J. M. Kincaid, J. Stat. Phys. 24, 469 (1981).Google Scholar
  6. 6.
    G. A. Baker, Jr., J. Stat. Phys. 77, 955 (1994).ADSMATHCrossRefGoogle Scholar
  7. 7.
    G. A. Baker, Computer Simulation Studies in Condensed Matter Physics 7, eds. D. P. Landau, K.K. Mon and H.-B. Schüttler, (( Springer, New York, 1994 ) pg. 213Google Scholar
  8. 8.
    R. H. Swendsen and J. S. Wang, Phys. Rev. Letts. 58, 86 (1987)ADSCrossRefGoogle Scholar
  9. 9.
    F. Cooper, B. Freedman, and D. Preston, Nucl. Phys. B210 [FS6], 210 (1991)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • G. A. BakerJr.
    • 1
    • 2
  • N. Kawashima
    • 3
  1. 1.Theoretical DivisionUniversity of CaliforniaLos AlamosUSA
  2. 2.Los Alamos National LaboratoryUniversity of CaliforniaLos AlamosUSA
  3. 3.University of TokyoJapan

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