Skip to main content
Log in

Low temperature expansion for continuous-spin Ising models

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

Abstract

We consider general ferromagnetic spin systems with finite range interactions and an even single-spin distribution of compact support on IR. It is shown under mild assumptions on the single-spin distribution that a low temperature expansion, in powers ofT, for the free energy and the correlation functions is asymptotic. We also prove exponential clustering in the pure phases and analyticity of the free energy and of the correlation functions in the reciprocal temperature β for Re β large.

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

Access this article

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. Minlos, R.A., Sinai, Y.: Trans. Moscow Math. Soc.17, 237 (1967); Math. USSR-Sbornik2, 355 (1967); Trans. Moscow Math. Soc.19, 121 (1968)

    Google Scholar 

  2. Glimm, J., Jaffe, A., Spencer, T.: Ann. of Phys.101, 610–630, 631–669 (1976)

    Article  Google Scholar 

  3. Gallavotti, G., Martin-Löf, A., Miracle-Sole, S.: In: Statistical mechanics and mathematical problems. Battelle Recontres 1971. Lecture Notes in Physics, Vol. 20. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  4. Bricmont, J., Pfister, C.E., Lebowitz, J.L.: Periodic Gibbs states of ferromagnetic spin systems J. Stat. Phys. (to appear)

  5. Lebowitz, J.L.: Number of phases in one component ferromagnets. In: Mathematical problems in theoretical physics, Proceedings, Rome 1977. Springer Lecture Notes in Physics No. 80

  6. Wells, D.: Some moment inequalities and a result on multivariate unimodality. Thesis. Indiana University, 1977

  7. Bortz, A., Griffiths, R.B.: Commun. Math. Phys.26, 102 (1972)

    Article  Google Scholar 

  8. Griffiths, R.B.: Phase transitions. In: Les Houches Lectures 1970. De Witt, C., Stora, R. (eds.) New York: Gordon and Breach 1971

    Google Scholar 

  9. Kunz, H., Souillard, B.: Commun. Math. Phys. (to appear)

  10. Lebowitz, J.L.: Commun. Math. Phys.28, 313 (1972)

    Article  Google Scholar 

  11. Schor, R.: Commun. Math. Phys.53, 213 (1978)

    Article  Google Scholar 

  12. Holsztynski, W., Slawny, J.: Commun. Math. Phys.66, 147 (1973)

    Article  Google Scholar 

  13. Gruber, C.: General lattice systems. In: Proc. 2nd Int. Coll. on Group Theoretical Methods in Physics, Nijmegen 1973. Janner, A., Janssen, T. (eds.). Nijmegen (1974)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Supported in part by N.S.F. Grant No. Phy. 78-15920 and MCS 78-01885

On leave from: Départment de Physique Théorique, Université de Louvin, Belgium

Supported in part by the Swiss National Foundation for Scientific Research

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bricmont, J., Lebowitz, J.L. & Pfister, C.E. Low temperature expansion for continuous-spin Ising models. Commun.Math. Phys. 78, 117–135 (1980). https://doi.org/10.1007/BF01941973

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01941973

Keywords

Navigation