Observables at infinity and states with short range correlations in statistical mechanics View Full Text


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Article Info

DATE

1969-09

AUTHORS

O. E. Lanford, D. Ruelle

ABSTRACT

We say that a representation of an algebra of local observables has short-range correlations if any observable which can be measured outside all bounded sets is a multiple of the identity, and that a state has finite range correlations if the corresponding cyclic representation does. We characterize states with short-range correlations by a cluster property. For classical lattice systems and continuous systems with hard cores, we give a definition of equilibrium state for a specific interaction, based on a local version of the grand canonical prescription; an equilibrium state need not be translation invariant. We show that every equilibrium state has a unique decomposition into equilibrium states with short-range correlations. We use the properties of equilibrium states to prove some negative results about the existence of metastable states. We show that the correlation functions for an equilibrium state satisfy the Kirkwood-Salsburg equations; thus, at low activity, there is only one equilibrium state for a given interaction, temperature, and chemical potential. Finally, we argue heuristically that equilibrium states are invariant under time-evolution. More... »

PAGES

194-215

References to SciGraph publications

  • 1967-10. Statistical mechanics of lattice systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1967-10. A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1966-12. A theorem on canonical commutation and anticommutation relations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1968-12. Statistical mechanics of quantum spin systems. III in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1968-12. Correlation functions of a lattice system in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1966-06. Invariant states in statistical mechanics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1966-04. States of physical systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1968-09. The classical mechanics of one-dimensional systems of infinitely many particles in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1966-02. Covariance algebras in field theory and statistical mechanics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1967-02. Large groups of automorphisms of C*-algebras in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01645487

    DOI

    http://dx.doi.org/10.1007/bf01645487

    DIMENSIONS

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