Abstract
The tree graph bound of Battle and Federbush is extended and used to provide a simple criterion for the convergence of (iterated) Mayer expansions. As an application estimates on the radius of convergence of the Mayer expansion for the two-dimensional Yukawa gas (nonstable interaction) are obtained.
Similar content being viewed by others
References
G. Benfatto,J. Stat. Phys. 41:671 (1985).
J. Fröhlich, Classical and quantum statistical mechanics in one and two dimensions: Two component Yukawa and Coulomb systems,Commun. Math. Phys. 47:233 (1976).
D. Brydges and P. Federbush, Debye Screening,Commun. Math. Phys. 73:197 (1980).
M. Göpfert and G. Mack, Iterated Mayer expansion for classical Gases at low temperatures,Commun. Math. Phys. 81:97 (1981); see also J. Imbrie, Iterated Mayer expansions and their application to Coulomb gases, inScaling and Self-Similarity in Physics—Renormalization in Statistical Mechanics and Dynamics, J. Fröhlich, ed. (Birkhäuser Boston, 1983).
M. Göpfert and G. Mack, Proof of confinement of static quarks in 3-dimensionalU(1) lattice gauge theory for all values of the coupling constant,Commun. Math. Phys. 82 (1982).
G. Battle and P. Federbush, A phase cell expansion for Euclidean field theories,Ann. Phys. 142:95 (1982); see also G. A. Battle, P. Federbush, and R. W. Robinson, Tree graphs and quasi-bounded spin systems, preprint.
D. Ruelle,Statistical Mechanics (Benjamin, London, 1969).
D. Brydges, A short course on cluster expansions, inProceedings of 1984 Les Houches Summer School, K. Osterwalder, ed., to be published by North-Holland.
D. Brydges and P. Federbush, A new form of the Mayer expansion in statistical mechanics,J. Math. Phys. 19:2064 (1978); see also Ref. 8.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brydges, D.C. Convergence of Mayer expansions. J Stat Phys 42, 425–435 (1986). https://doi.org/10.1007/BF01127719
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01127719