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Existence and uniqueness of equilibrium states for some spin and continuum systems

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Abstract

The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnetis is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture ofA –B particles in which there is no interaction between like particles and a repulsion between unlike particles. Where the derivative of the free energy is discontinuous there are at least two equilibrium states.

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Authors and Affiliations

  1. Istituto di Fisica, Università di Roma, Rome, Italy

    M. Cassandro

  2. Istituto Nazionale di Fisica Nucleare — Sezione di Roma, Italy

    M. Cassandro

  3. Istituto di Fisica Teorica — Università di Napoli, Italy

    G. Gallavotti

  4. Belfer Graduate School of Science, Yeshiva University, New York, N.Y., USA

    J. L. Lebowitz

  5. Dept. of Physics Columbia University, New York, N.Y., USA

    J. L. Monroe

Authors
  1. M. Cassandro
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  2. G. Gallavotti
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  3. J. L. Lebowitz
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  4. J. L. Monroe
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Additional information

Supported in part by Air Force Grant n. 732430.

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Cassandro, M., Gallavotti, G., Lebowitz, J.L. et al. Existence and uniqueness of equilibrium states for some spin and continuum systems. Commun.Math. Phys. 32, 153–165 (1973). https://doi.org/10.1007/BF01645653

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  • DOI: https://doi.org/10.1007/BF01645653

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