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Some Monte-Carlo Studies of the Ising Model

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Computer Simulation Studies in Condensed-Matter Physics VII

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 78))

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Abstract

The Markov property method of speeding up standard Monte Carlo methods can yield about an order of magnitude improvement for the two-dimensional Ising model. We also study the effects of finite size in the three-dimensional Ising model on the computation of the renormalized coupling constant and find, so long as the correlation length is less that about one-tenth the system width, that an accuracy of one percent or better can be expected.

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References

  1. G. A. Baker, Jr., A Markov-Property, Monte-Carlo Method: One Dimensional Ising Model, J. Stat. Phys. 72 (1993), 621.

    Article  MATH  ADS  Google Scholar 

  2. G.A. Baker, rJr., The Markov-Property Method Applied to Ising Model Calculations, Los Alamos preprint, submitted for publication.

    Google Scholar 

  3. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21 (1953), 1087.

    Article  ADS  Google Scholar 

  4. R. H. Swendsen and J.-S. Wang, Nonuniversal Critical Dynamics in Monte Carlo Simulations, Phys. Rev. Letts. 58 (1987), 86.

    Article  ADS  Google Scholar 

  5. N. Madras and A. D. Sokal, The Pivot Algorithm: A Highly Efficient Monte Carlo Method for the Self-Avoiding Walk, J. Stat. Phys. 50 (1988), 109.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. D. Stauffer, Ising-Model Relaxation as Testing Ground for Modern Computers, Computer Simulation Studies in Condensed-Matter Physics VI, D. P. Landau, K. K. Mon, and H.-B. Schüttler, eds., Springer-Verlag, 1993, Berlin.

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  7. B. Dammann and J. D. Reger, Dynamical Critical Exponent of the Two Dimensional hing Model, Johannes Gutenberg-Universität Mainz preprint, (1992).

    Google Scholar 

  8. G. A. Baker, Jr., Analysis of hyperscaling in the hing Model by the high-temperature series method, Phys. Rev. B 15 (1977), 1552–1559.

    Article  ADS  Google Scholar 

  9. B. A. Freedman and G. A. Baker, Jr., A test for hyperscaling violation in the three-dimensional hing model, J. Phys. A15 (1982), L715.

    ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, University of California, Los Alamos, NM, 87545, USA

    G. A. Baker Jr. & J. J. Erpenbeck

Authors
  1. G. A. Baker Jr.
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  2. J. J. Erpenbeck
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Editor information

Editors and Affiliations

  1. Center for Simulational Physics, The University of Georgia, Athens, GA, 30602, USA

    David P. Landau Ph. D. , K. K. Mon Ph. D  & Heinz-Bernd Schüttler Ph. D. ,  & 

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© 1994 Springer-Verlag Berlin Heidelberg

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Baker, G.A., Erpenbeck, J.J. (1994). Some Monte-Carlo Studies of the Ising Model. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics VII. Springer Proceedings in Physics, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79293-9_23

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  • DOI: https://doi.org/10.1007/978-3-642-79293-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-79295-3

  • Online ISBN: 978-3-642-79293-9

  • eBook Packages: Springer Book Archive

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