Skip to main content
SpringerLink
Log in

Renormalization group study of a critical lattice model

I. Convergence to the line of fixed points

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We start a nonperturbative study of the Wilson-Kadanoff renormalization group (RG) in weakly coupled massless lattice models. Nonlocal hierarchical models are introduced to mimic the infrared behaviour of the\(\tfrac{1}{2}(\nabla \phi )^2 + \lambda (\nabla \phi )^4\) model and the like. The RG is shown to drive these to the line of fixed points corresponding to the massless\(\tfrac{1}{2}c_\infty (\lambda )(\nabla \phi )^2\) models.

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. Balaban, T., Gawedzki, K.: A low temperature expansion for the pseudoscalar Yukawa model of quantum fields in two space-time dimensions. Preprint. Harvard University

  2. Bleher, P.M., Sinai, Ya.G.: Commun. Math. Phys.33, 23–42 (1973)

    Google Scholar 

  3. Bricmont, J., Fontaine, J.-R., Lebowitz, J.L., Spencer, T.: Commun. Math. Phys.78, 281–302 (1980)

    Google Scholar 

  4. Bricmont, J., Fontaine, J.-R., Lebowitz, J.L., Spencer, T.: Commun. Math. Phys.78, 363–372 (1981)

    Google Scholar 

  5. Bricmont, J., Fontaine, J.-R., Lebowitz, J.L., Lieb, E.H., Spencer, T.: Commun. Math. Phys.78, 545–566 (1981)

    Google Scholar 

  6. Duneau, M., Iagolnitzer, D., Souillard, B.: Commun. Math. Phys.31, 191–208 (1973)

    Google Scholar 

  7. Federbush, P.G.: A mass zero cluster expansion. Part I. The expansion. Part 2. Convergence. Commun. Math. Phys.81, 327–340 and 341–360 (1981)

    Google Scholar 

  8. Fröhlich, J., Spencer, T.: On the statistical mechanics of class of Coulomb and dipole gases. Preprint. IHES: Bures-sur-Yvette

  9. Fröhlich, J., Spencer, T.: Phase diagrams and critical properties of (classical) Coulomb systems. Preprint, IHES, Bures-sur-Yvette

  10. Gallavotti, G., Miracle-Sole, S.: Commun. Math. Phys.7, 274–288 (1968)

    Google Scholar 

  11. Gawedzki, K., Kupiainen, A.: Commun. Math. Phys.77, 31–64 (1980)

    Google Scholar 

  12. Glimm, J., Jaffe, A.: Fortschr. Phys.21, 327–376 (1973)

    Google Scholar 

  13. Griffiths, R.B., Pearce, P.A.: J. Stat. Phys.20, 499–545 (1979)

    Google Scholar 

  14. Higuchi, Y., Lang, R.: On convergence of the Kadanoff transformation towards trivial fixed points. Preprint. Institute for Applied Mathematics, Heidelberg

  15. Iagolnitzer, D., Souillard, B.: Commun. Math. Phys.60, 131–152 (1978)

    Google Scholar 

  16. Israel, R.B.: Banach algebras and Kadanoff transformations. Preprint. University of British Columbia

  17. Gawedzki, K., Kupiainen, A.: To be published

  18. Kunz, H.: Commun. Math. Phys.59, 53–69 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Methods of Physics, Warsaw University, PL-00-682, Warsaw, Poland

    K. Gawedzki

  2. Research Institute for Theoretical Physics, Helsinki University, SF-00170, Helsinki 17, Finland

    A. Kupiainen

Authors
  1. K. Gawedzki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Kupiainen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gawedzki, K., Kupiainen, A. Renormalization group study of a critical lattice model. Commun.Math. Phys. 82, 407–433 (1981). https://doi.org/10.1007/BF01237048

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01237048

Keywords

Search

Navigation