Communications in Mathematical Physics

, Volume 59, Issue 3, pp 235–266

Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems

Authors

  • Jürg Fröhlich
    • Department of MathematicsPrinceton University
  • Yong Moon Park
    • Department of MathematicsYonsei University
Article

DOI: 10.1007/BF01611505

Cite this article as:
Fröhlich, J. & Park, Y.M. Commun.Math. Phys. (1978) 59: 235. doi:10.1007/BF01611505

Abstract

We use Ginibre's general formulation of Griffiths' inequalities to derive new correlation inequalities for two-component classical and quantum mechanical systems of distinguishable particles interacting via two body potentials of positive type. As a consequence we obtain existence of the thermodynamic limit of the thermodynamic and correlation functions in the grand canonical ensemble at arbitrary temperatures and chemical potentials. For a large class of systems we show that the limiting correlation functions are clustering. (In a subsequent article these results are extended to the correlation functions of two-component quantum mechanical gases with Bose-Einstein statistics). Finally, a general construction of the thermodynamic limit of the pressure for gases which are not H-stable, above collapse temperature, is presented.

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© Springer-Verlag 1978