We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be aK-system.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Arnold, V. I., etA. Avez: Problèmes ergodiques de la mécanique classique. Paris: Gauthier-Villars 1967.
Fisher, M. E.: The theory of condensation (Sec. 6.). Lecture given at the Centennial Conference on Phase Transformation at the University of Kentucky, 1965.
Jacobs, K.: Lecture notes on ergodic theory. Aarhus Universitet (1962–1963).
Robinson, D., andD. Ruelle: Mean entropy of states in classical statistical mechanics. Commun. Math. Phys.5, 288–300 (1967).
van Hove, L.: L'intégrale de configuration pour les systèmes de particules à une dimension. Physica16, 137–143 (1950).
About this article
Cite this article
Ruelle, D. Statistical mechanics of a one-dimensional lattice gas. Commun.Math. Phys. 9, 267–278 (1968). https://doi.org/10.1007/BF01654281
- Neural Network
- Phase Transition
- Dynamical System
- Statistical Physic
- Equilibrium State