On the Wulff Construction as a Problem of Equivalence of Statistical Ensembles

  • Salvador Miracle-Sole
  • Jean Ruiz
Part of the NATO ASI Series book series (NSSB, volume 324)

Abstract

In this note, the statistical mechanics of SOS (solid-on-solid) 1-dimensional mod els under the global constraint of having a specified area between the interface and the horizontal axis, is studied. We prove the existence of the thermodynamic limits and the equivalence of the corresponding statistical ensembles. This gives a simple alter native microscopic proof of the validity of the Wulff construction for such models, first established in Ref. 1.

Keywords

Entropy Librium 

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References

  1. 1.
    J. De Coninck, F. Dunlop and V. Rivasseau, On the microscopic validity of the Wulff construction and of the generalized Young equation, Commun. Math. Phys. 121, 401–419 (1989).ADSMATHCrossRefGoogle Scholar
  2. 2.
    R. L.Dobrushin, R. Kotecký and S.B.Shlosman, “Wulff Construction: A Global Shape from Local Interactions,” Am.Math.Soc., Providence, RI (1992).Google Scholar
  3. 3.
    A. Messager, S. Miracle-Sole and J. Ruiz, Convexity properties of the surface tension and equi librium crystals, J. Stat. Phys. 67, 449–470 (1992).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    D.Ruelle, “ Statistical Mechanics: Rigorous Results,” Benjamin, New York Amsterdam (1969).MATHGoogle Scholar
  5. 5.
    L. Galgani, L. Manzoni, and A. Scotti, Asymptotic equivalence of equilibrium ensembles of clas sical statistical mechanics, J. Math. Phys. 12, 933–935 (1971).ADSCrossRefGoogle Scholar
  6. 6.
    D.Ruelle, “Hasard et Chaos” (chap. 19), Odile Jacob, Paris (1991). O.Landford, Entropy and equilibrium states in classical statistical mechanics, in: “Statistical Mechanics and Mathematical Problems,” A. Lenard, ed., Springer, Berlin (1973).Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Salvador Miracle-Sole
    • 1
  • Jean Ruiz
    • 1
  1. 1.Centre de Physique ThéoriqueCNRS Luminy Case 907Marseille, Cedex 9France

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