Abstract
A study is made of the statistical mechanics of classical lattice spin systems with finite-range interactions in two dimensions. By means of a decimation procedure, a finite-size condition is given for the convergence of a cluster expansion that is believed to be useful for treating the range of temperature between the critical oneT c and the estimated thresholdT 0 of convergence of the usual high-temperature expansion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Cammarota,Commun. Math. Phys. 85:517 (1982).
M. Campanino, D. Capocaccia, and E. Olivieri,J. Slat. Phys. 33:437 (1983).
M. Cassandro and E. Olivieri,Commun. Math. Phys. 80:255 (1981).
R. L. Dobrushin and S. B. Shlosman, inStatistical Physics and Dynamical Systems, D. Szasz and D. Petz, eds. (Birkhäuser, Boston, 1985).
R. L. Dobrushin and S. B. Shlosman, inStatistical Physics and Dynamical Systems, D. Szasz and D. Petz, eds. (Birkhäuser, Boston, 1985).
G. Gallavotti and S. Miracle-Sole,Commun. Math. Phys. 7:274 (1968).
G. Gallavotti, A. Martin Löf, and S. Miracle-Sole, inBattelle Seattle 1971 Rencontres, A. Lenard, ed. (Lecture Notes in Physics, Vol. 20, Springer, Berlin, 1973), pp. 162–204.
Ch. Gruber and H. Kunz,Commun. Math. Phys. 22:133 (1971).
L. Kadanoff and A. Hoghton,Phys. Rev. B 11:377 (1975).
R. Kotecky and D. Preiss,Commun. Math. Phys. 103:491 (1986).
L. Russo,Z. Wahrs. V. Geb. 61:129 (1982).
R. L. Dobrushin and S. B. Shlosman,J. Stat. Phys. 46:983 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Olivieri, E. On a cluster expansion for lattice spin systems: A finite-size condition for the convergence. J Stat Phys 50, 1179–1200 (1988). https://doi.org/10.1007/BF01019160
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01019160