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Statistical mechanics of systems of unbounded spins

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Abstract

We develop the statistical mechanics of unboundedn-component spin systems on the latticeZ v interacting via potentials which are superstable and strongly tempered. We prove the existence and uniqueness of the infinite volume free energy density for a wide class of boundary conditions. The uniqueness of the equilibrium state (whose existence is established in general) is then proven for one component ferromagnetic spins whose free energy is differentiable with respect to the magnetic field.

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References

  1. Simon, B.: TheP(ø) r Euclidean (quantum) field theory. Princeton, N.J.: Princeton University Press 1974

    Google Scholar 

  2. Guerra, F., Rosen, L., Simon, B.: Ann. Math.101, N. 1, 2 (1975)

    Google Scholar 

  3. Glimm, J., Jaffe, A., Spencer, T.: Reports at the Kyoto, Marseille, Bielefeld conferences

  4. Ruelle, D.: Statistical mechanics: rigorous results. Benjamin: New York 1969

    Google Scholar 

  5. Ruelle, D.: Commun. math. Phys.12, 127–159 (1970)

    Google Scholar 

  6. Ruelle, D.: Probability estimates for continuous spin systems. Preprint

  7. Lebowitz, J. L., Martin, Löf, A.: Commun. math. Phys.25, 276–282 (1972)

    Google Scholar 

  8. Frohlich, J., Simon, B.: Private communication

  9. Lebowitz, J. L.: Proceedings of the Kyoto conference. Berlin-Heidelberg-New York: Springer

  10. Lanford III, O. E.: Battelle conference 1974

  11. Dobrushin, R. L.: Funkts. Anal. Ego Pril.2, 31 (1968);2, 44 (1968)

    Google Scholar 

  12. Lanford III, O. E., Ruelle, D.: Commun. math. Phys.13, 194 (1969)

    Google Scholar 

  13. Ruelle, D.: see Ref. 4

    Google Scholar 

  14. Fortuin, C., Kasteleyn, P., Ginibre, J.: Commun. math. Phys:22, 89–103 (1971)

    Google Scholar 

  15. Lee, T. D., Yang, C. N.: Phys. Rev.87, 410–419 (1952)

    Google Scholar 

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Authors and Affiliations

  1. Belfer Graduate School of Science, Yeshiva University, 10033, New York, N.Y., USA

    Joel L. Lebowitz

  2. Istituto Mathematico Università, dell'Aquila, L'Aquila, Italy

    Errico Presutti

Authors
  1. Joel L. Lebowitz
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  2. Errico Presutti
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Communicated by G. Gallavotti

Communicated by G. Gallavotti

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Lebowitz, J.L., Presutti, E. Statistical mechanics of systems of unbounded spins. Commun.Math. Phys. 50, 195–218 (1976). https://doi.org/10.1007/BF01609401

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  • DOI: https://doi.org/10.1007/BF01609401

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