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A note on the stability of phase diagrams in lattice systems

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Abstract

We construct a class of non-symmetry breaking pair interactions, which change the phase diagram of then.n. Ising and classicalX Y model. Furthermore we improve earlier obtained constraints on the decrease of interactions, necessary to get analyticity properties of the pressure in manifolds of non-symmetry breaking interactions.

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References

  1. Daniëls, H. A. M., Enter, A. C. D. van: Commun. Math. Phys.71, 65–76 (1980)

    Google Scholar 

  2. Pirogov, S. A., Sinai, Ya. G.: Theor. Math. Phys. USSR25, 358–369 (1975),26, 61–76 (1976)

    Google Scholar 

  3. Ginibre, J., Grossmann, A., Ruelle, D.: Commun. Math. Phys.3, 187–193 (1966)

    Google Scholar 

  4. Israel, R. B.: Convexity in the theory of lattice gases. Princeton, NJ: Princeton University Press 1979

    Google Scholar 

  5. Lanford, O., Ruelle, D.: Commun. Math. Phys.13, 194–215 (1969)

    Google Scholar 

  6. Kastler, D., Robinson, D. W.: Commun. Math. Phys.3, 151–180 (1966)

    Google Scholar 

  7. Messager, A., Miracle-Sole, S.: Commun. Math. Phys.40, 187–196 (1975)

    Google Scholar 

  8. Iagolnitzer, D., Souillard, B.: Contribution to the Esztergom 1979. Conference on Random fields (to appear)

  9. Iagolnitzer, D., Souillard, B.: Commun. Math. Phys.60, 131–152 (1978)

    Google Scholar 

  10. Simon, B.: Private Communication

  11. Ruelle, D.: Statistical mechanics, New York, Amsterdam: Benjamin (1969)

    Google Scholar 

  12. Ruelle, D.: Commun. Math. Phys.3, 133–150 (1966)

    Google Scholar 

  13. Aizenman, M.: Phys. Rev. Lett.43, 407–409 (1979)

    Google Scholar 

  14. Brascamp, H. J.: Commun. Math. Phys.18, 82–96 (1970)

    Google Scholar 

  15. Fröhlich, J., Simon B., Spencer T.: Commun. Math. Phys.50, (1976)

  16. Griffiths, R. B., Pearce, P. A.: Phys. Rev. Lett.41, (1978); J. Stat. Phys.20, 444 (1979)

    Google Scholar 

  17. Israel, R. B.: Proceedings Esztergom Conference on Random Fields (to appear)

  18. Hille, E., Phillips, R.: Functional analysis and semigroups. Chap. III, Sect. 17. Baltimore: Waverly Press (1959)

    Google Scholar 

  19. Enter, A. C. D. van: (to be published)

  20. Ruelle, D.: Symmetry breakdown in statistical mechanics. In: Cargèse Lectures in Physics, Vol. 4, Kastler, D. (ed.) pp. 169–194. New York, London, Paris: Gordon and Breach 1970

    Google Scholar 

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Communicated by E. Lieb

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van Enter, A.C.D. A note on the stability of phase diagrams in lattice systems. Commun.Math. Phys. 79, 25–32 (1981). https://doi.org/10.1007/BF01208283

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