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The phase separation line in the two-dimensional Ising model

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Abstract

We prove that, at low temperature, the line of separation between the two pure phases shows large fluctuations in shape. This implies the translation invariance of the correlation functions associated with some non translation invariant boundary conditions and should be a peculiarity of the dimensionality of the model.

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References

  1. Dobrushin, R. L.: Functional Anal. Appl.8, 302 (1968) (English edition, see p. 309).

    Google Scholar 

  2. Minlos, R.: Russian Math. Surveys23, 137 (1968).

    Google Scholar 

  3. Gallavotti, G.: talk at the 1971 S.I.F. meeting. Internal report of the physics Dept. of the Univ. of Roma no 347. To appear in Riv. Nuovo Cimento.

  4. —— Miracle-Sole, S.: Equilibrium states of the Ising model in the two phase region. Phys. Rev.5 B, 2555 (1972).

    Google Scholar 

  5. Minlos, R., Sinai, Ya.: Math. Sbornik73, 115 (1967).

    Google Scholar 

  6. See [4], see also R. B. Griffiths: Phys. Rev.152, 240 (1966) and A. Martin-Lof: preprint.

    Google Scholar 

  7. Gallavotti, G., Miracle-Sole, S.: Commun. math. Phys.7, 274 (1968).

    Google Scholar 

  8. See [3].

  9. ——, Martin-Löf, A.: Surface tension in the two dimensional Ising model. Commun. math. Phys.25, 87–126 (1972).

    Google Scholar 

  10. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969; p. 83 and p. 86; see also [7] p. 285–288.

    Google Scholar 

  11. Fisz, M.: Probability theory and mathematical statistics III. edition, p. 211. New York: J. Wiley.

  12. Kolmogorov, A. N.: Selected translations in Math. Statistics and Probability. IMS and AMS 1962 (translation of the AMS) p. 109.

  13. Spitzer, F.: Am. Math. Monthly78, 142 (1971).

    Google Scholar 

  14. Van Beyeren, H.: private communication. To be published.

  15. The functions ϕ and ϕT of this section are obviously not the same as the ones of Theorem 2: there should be no confusion between them since they are defined on completely different spaces.

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Authors and Affiliations

  1. I.H.E.S., Bures sur Yvette, France

    Giovanni Gallavotti

  2. Istituto di Matematica, Università di Roma, Piazzale delle Scienze, I-00187, Roma, Italy

    Giovanni Gallavotti

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  1. Giovanni Gallavotti
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This work has been partially supported by the Consiglio Nazionale delle Ricerche (Gruppo Nazionale per l'Analisi Funzionale): CNR(GNAFA).

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Gallavotti, G. The phase separation line in the two-dimensional Ising model. Commun.Math. Phys. 27, 103–136 (1972). https://doi.org/10.1007/BF01645615

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  • DOI: https://doi.org/10.1007/BF01645615

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