Skip to main content
SpringerLink
Log in

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of “dangerous irrelevant variables” and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. P. Kadanoffet al., Rev. Mod. Phys. 39:395 (1967).

    Google Scholar 

  2. M. E. Fisher,J. Appl. Phys. 38:981 (1967).

    Google Scholar 

  3. M. E. Fisher,Rev. Mod. Phys. 46:597 (1974).

    Google Scholar 

  4. M. E. Fisher,Renormalization Group Methods in Statistical Physics and Field Theory (Proc. Conference Temple University), M. S. Green and J. D. Gunton, eds. (1973).

  5. P. C. Hemmer and J. L. Lebowitz, inPhase Transitions and Critical Phenomena, C. Domb and M. S. Green, eds. (Academic, New York, 1976), Vol. 5B, p. 107.

    Google Scholar 

  6. Th. Niemeijer and J. M. J. van Leeuwen, inPhase Transitions and Critical Phenomena, C. Domb and M. S. Green, eds. (Academic, New York, 1976), Vol. 6.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. F. J. Wegner,J. Phys. C 7:2098 (1974).

    Google Scholar 

  10. L. P. Kadanoff and A. Houghton,Phys. Rev. B 11:377 (1975).

    Google Scholar 

  11. H. E. Stanley,Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971).

    Google Scholar 

  12. K. G. Wilson,Phys. Rev. B 4:3184 (1971).

    Google Scholar 

  13. Th. Niemeyer and J. M. J. van Leeuwen,Physica 71:17 (1974).

    Google Scholar 

  14. S. Ma,Rev. Mod. Phys. 45:589 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut voor Theoretische Fysika, Universiteit van Nijmegen, Nijmegen, Netherlands

    H. J. F. Knops

  2. Laboratorium voor Technische Natuurkunde, Technische Hogeschool, Delft, Netherlands

    J. M. J. van Leeuwen

  3. Institutt for Teoretisk Fysikk, NTH, Universitetet i Trondheim, Trondheim, Norway

    P. C. Hemmer

Authors
  1. H. J. F. Knops
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. J. van Leeuwen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. C. Hemmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knops, H.J.F., van Leeuwen, J.M.J. & Hemmer, P.C. Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling. J Stat Phys 17, 197–214 (1977). https://doi.org/10.1007/BF01040102

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01040102

Key words

Search

Navigation