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Strict convexity (“continuity”) of the pressure in lattice systems

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Abstract

It is shown that the pressure is a strictly convex function of the translationally invariant interactions (under certain mild restrictions on the long-range part of these interactions) for classical and quantum lattice systems, by demonstrating that two distinct interactions can never lead to the same translationally invariant equilibrium state. This generalizes a previous result that the pressure is a continuous function of density at fixed temperature.

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Authors and Affiliations

  1. Battelle Seattle Research Center, Seattle, Washington

    Robert B. Griffiths & David Ruelle

  2. I.H.E.S., F-91 Bures-sur-Yvette, France

    Robert B. Griffiths

  3. Physics Department, Carnegie-Mellon University, 15213, Pittsburgh, Pennsylvania, USA

    David Ruelle

Authors
  1. Robert B. Griffiths
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  2. David Ruelle
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Griffiths, R.B., Ruelle, D. Strict convexity (“continuity”) of the pressure in lattice systems. Commun.Math. Phys. 23, 169–175 (1971). https://doi.org/10.1007/BF01877738

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  • DOI: https://doi.org/10.1007/BF01877738

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