Communications in Mathematical Physics

, Volume 9, Issue 4, pp 267–278 | Cite as

Statistical mechanics of a one-dimensional lattice gas

  • D. Ruelle


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.


Neural Network Phase Transition Dynamical System Statistical Physic Equilibrium State 
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Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • D. Ruelle
    • 1
  1. 1.I.H.E.S.91. Bures-sur-Yvette

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