Skip to main content
SpringerLink
Log in

Pfaffian bundles and the Ising model

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

Abstract

An infinite volume Pfaffian formalism is developed for the Ising model.

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. Atiyah, M., Singer, I.: Index theory for skew-adjoint Fredholm operators. Publ. Math. IHES,37, 305–326 (1969)

    Google Scholar 

  2. Baxter, R.: Phil. Trans. Roy. Soc.289A, 315 (1978)

    Google Scholar 

  3. Carey, A., O'Brien, D.: Automorphisms of the infinite dimensional Clifford algebra and the Atiyah-Singer mod 2 index. Topology22, 937–948 (1983)

    Google Scholar 

  4. Carey, A., Palmer, J.: Infinite complex spin groups. J. Funct. Anal. (to appear)

  5. Hurst, A.: The relation between the Onsager and the Pfaffian method for solving the Ising problem. I. The rectangular lattice. J. Math. Phys.6, 1 (1965)

    Google Scholar 

  6. Jaffe, A., Lesniewski, A., Weitsman, J.: Pfaffians on Hilbert space, Harvard preprint HUTMP B207 Oct. 27, 1987

  7. Kaufman, B.: Crystal statistics II. Partition function evaluated by spinor analysis. Phys. Rev.76, 1232–1243 (1949)

    Google Scholar 

  8. McCoy, B. M., Wu, T. T.: The two dimensional Ising Model. Cambridge, MA: Harvard University Press 1973

    Google Scholar 

  9. Onsager, L.: Crystal statistics I. A two dimensional model with an order disorder transition. Phys. Rev.65, 117–149 (1944)

    Google Scholar 

  10. Palmer, J.: Monodromy fields onZ 2. Commun. Math. Phys.102, 175–206 (1985)

    Google Scholar 

  11. Palmer, J., Tracy, C.: Two dimensional Ising correlations: Convergence of the scaling limit, Adv. Appl. Math.2, 329–388 (1981); Two dimensional Ising correlations: The SMJ analysis, Adv. Appl. Math.4, 46–102 (1983)

    Google Scholar 

  12. Perk, J., Au-Yang, H.: Solution of the Hirota discrete time Todas lattice equation and the critical correlations in theZ-invariant Ising model, Stony Brook preprint

  13. Pressley, A., Segal, G.: Loop groups. Oxford: Clarendon Press 1986

    Google Scholar 

  14. Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. Funct. Anal. Appl.19, 31–34 (1985)

    Google Scholar 

  15. Simon, B.: Notes on infinite determinants of Hilbert space operators. Adv. Math.24, 244–273 (1977)

    Google Scholar 

  16. Segal, G., Wilson, G.: Loop groups and equations of KdV type. Pub. Math. IHES,61, 5–65 (1985)

    Google Scholar 

  17. Sato, M., Miwa, T., Jimbo, M.: Holonomic quantum fields V. Publ. RIMS, Kyoto Univ.16, 531–584 (1980)

    Google Scholar 

  18. Witten, E.: Quantum field theory, Grassmannians, and algebraic curves. Commun. Math. Phys.113, 529–600 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tucson, Arizona, USA

    John Palmer

Authors
  1. John Palmer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by K. Gawedzki

Research supported in part by NSF grant DMS-8421289

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palmer, J. Pfaffian bundles and the Ising model. Commun.Math. Phys. 120, 547–574 (1989). https://doi.org/10.1007/BF01260387

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01260387

Keywords

Search

Navigation