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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Communicated by E. Lieb
Research supported in part by the U.S. National Science Foundation under grant MPS 75-11864
A Sloan Foundation Fellow
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Fröhlich, J., Park, Y.M. Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems. Commun.Math. Phys. 59, 235–266 (1978). https://doi.org/10.1007/BF01611505
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DOI: https://doi.org/10.1007/BF01611505