Communications in Mathematical Physics

, Volume 59, Issue 3, pp 235-266

First online:

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

  • Jürg FröhlichAffiliated withDepartment of Mathematics, Princeton University
  • , Yong Moon ParkAffiliated withDepartment of Mathematics, Yonsei University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.