Abstract
A class of one-dimensional classical lattice gas models with translationally invariant, stable and strongly tempered many-body interactions, is constructed for which the limiting thermodynamic pressure is a discontinuous function of the density (at fixed temperature). This demonstrates that an apparently “mild” restriction on the potential (“supersummability”) employed by Griffiths and Ruelle in proving the continuity of the pressure in lattice systems, plays, in fact, a crucial role.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ruelle, D.: Helv. Phys. Acta36, 183 (1963).
Dobrushin, R. L., Minlos, R. A.: Teor. Veroyat. Ee Primen.12, 596 (1967) [English transl.: Theory Prob. Appl.12, 535 (1967)].
Ginibre, J.: Phys. Lett.24 A, 223 (1967); Phys. Rev. Letters24, 1473 (1970).
Ruelle, D.: Commun. math. Phys.18, 127 (1970).
Griffiths, R. B., Ruelle, D.: Commun. math. Phys.23, 169 (1971).
Fisher, M. E.: Arch. Rat. Mech. Anal.17, 377 (1964).
Ruelle, D.: Statistical mechanics: Rigorous results. New York: W. A. Benjamin, Inc. 1969.
Fisher, M. E.: Physics3, 255 (1967).
—— In: Systemes a un nombre infini de degrés de liberté. Colloq. Internat. du C.N.R.S. No. 181, p. 87. Paris: Edition C.N.R.S. 1970.
—— Felderhof, B. U.: Ann. Phys. (N.Y.)58, 176, 217, 268 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fisher, M.E. On discontinuity of the pressure. Commun.Math. Phys. 26, 6–14 (1972). https://doi.org/10.1007/BF01877543
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01877543