Skip to main content
SpringerLink
Log in
Book cover

Computer Simulation Studies in Condensed-Matter Physics XIV pp 102–110Cite as

The Spectrum of Eigenvalues in the Renormalization Group Theory of Phase Transitions

  • Conference paper

  • 196 Accesses

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 89))

Abstract

It is shown that for any two eigenvalues of a general renormalization group transformation, there exists an eigenoperator with eigenvalue equal to the product of those two eigenvalues. Corrections to scaling are generated by such product operators - even at a fixed point - with exactly the same set of exponents derived by Wegner. Because of these operators, renormalized couplings are not generally expected to be analytic functions of the original couplings, but include terms of the form (K – K c )2-α. Methods for performing numerical tests of all results are described.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.G. Wilson and J. Kogut: Phys. Reports C 12, 75 (1974).

    Article  ADS  Google Scholar 

  2. R.H. Swendsen: Phys. Rev. Lett. 52, 2321 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  3. M.E. Fisher and M. Randeria: Phys. Rev. Lett. 56, 2332 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  4. F.J. Wegner: Phys. Rev B 5, 4529 (1972).

    Article  ADS  Google Scholar 

  5. A. Aharony and M.E. Fisher: Phys. Rev. B 27, 4394 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  6. R.H. Swendsen: Phys. Rev. Lett. 52, 1165 (1984); Phys. Rev. B 30, 3875 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  7. R. Gupta and R. Cordery: Phys. Lett. 105A, 415 (1984).

    ADS  Google Scholar 

  8. H.W.J Blöte, J.R. Heringa, A. Hoogland, E.W. Meyer, and T.S. Smit: Phys. Rev. Lett. 76, 2613 (1996).

    Article  ADS  Google Scholar 

  9. R.H. Swendsen, Monte Carlo Renormalizaiton in Real-Space Renormalization, ed. by T.E. Burkhardt and J.M.J. van Leeuwen (Topicas in Current Physics, Vol. 30) (Springer, Berlin Heidelberg New York 1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    R. H. Swendsen

Authors
  1. R. H. Swendsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Simulational Physics, The University of Georgia, 30602-2451, Athens, GA, USA

    David P. Landau Ph.D. , Steven P. Lewis Ph.D.  & Heinz-Bernd Schüttler Ph.D. ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Swendsen, R.H. (2002). The Spectrum of Eigenvalues in the Renormalization Group Theory of Phase Transitions. In: Landau, D.P., Lewis, S.P., Schüttler, HB. (eds) Computer Simulation Studies in Condensed-Matter Physics XIV. Springer Proceedings in Physics, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59406-9_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59406-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63967-8

  • Online ISBN: 978-3-642-59406-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation