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.
Similar content being viewed by others
References
Minlos, R.A., Sinai, Y.: Trans. Moscow Math. Soc.17, 237 (1967); Math. USSR-Sbornik2, 355 (1967); Trans. Moscow Math. Soc.19, 121 (1968)
Glimm, J., Jaffe, A., Spencer, T.: Ann. of Phys.101, 610–630, 631–669 (1976)
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
Bricmont, J., Pfister, C.E., Lebowitz, J.L.: Periodic Gibbs states of ferromagnetic spin systems J. Stat. Phys. (to appear)
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
Wells, D.: Some moment inequalities and a result on multivariate unimodality. Thesis. Indiana University, 1977
Bortz, A., Griffiths, R.B.: Commun. Math. Phys.26, 102 (1972)
Griffiths, R.B.: Phase transitions. In: Les Houches Lectures 1970. De Witt, C., Stora, R. (eds.) New York: Gordon and Breach 1971
Kunz, H., Souillard, B.: Commun. Math. Phys. (to appear)
Lebowitz, J.L.: Commun. Math. Phys.28, 313 (1972)
Schor, R.: Commun. Math. Phys.53, 213 (1978)
Holsztynski, W., Slawny, J.: Commun. Math. Phys.66, 147 (1973)
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)
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01941973