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The geometrical phase transitions in a lattice model

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Abstract

We shall consider a finite range model on a square latticeZ 3 and show the existence of bubble, tubular and lamellar phases by estimating the correlation functions at low temperature.

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References

  1. Minlos, R.A., Sinai, Ja.G.: Mat. Sb.73, 115 (1967)

    Google Scholar 

  2. Minlos, R.A., Sinai, Ja.G.: Trans. Moscow Math. Soc.19, 121 (1968)

    Google Scholar 

  3. Heilmann, O.J.: Commun. Math. Phys.36, 91 (1974)

    Google Scholar 

  4. Gertsik, V.M., Dobrushin, R.L.: Funkts. Anal.8, 12 (1972)

    Google Scholar 

  5. Tachibana, T., Kobayashi, K., Suzuki, H., Honda, K., Sukigara, M.: Liquid crystal. Tokyo: Kyoritsu 1972 (in Japanese)

    Google Scholar 

  6. Peierls, R.E.: Proc. Cambridge Philos. Soc.32, 477 (1936)

    Google Scholar 

  7. Dobrushin, R.L.: Funct. Anal. Appl.8, 302 (1968)

    Google Scholar 

  8. Abraham, D.B., Heilmann, O.J.: J. Stat. Phys.4, 15 (1972)

    Google Scholar 

  9. Abraham, D.B., Heilmann, O.J.: J. Stat. Phys.13, 6, 461 (1975)

    Google Scholar 

  10. Gallavotti, G., Miracle-Sole, S.: Commun. Math. Phys.27, 103 (1972)

    Google Scholar 

  11. Minlos, R.: Russ. Math. Surv.23, 137 (1968)

    Google Scholar 

  12. Ruelle, D.: Statistical mechanics. Rigorous results. New York: Benjamin 1969

    Google Scholar 

  13. Miyamoto, M.: Phase transitions in lattice models. Seminar on Prob. (1972) (in Japanese)

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Authors and Affiliations

  1. Institute of Mathematics, University of Tsukuba, Sakuramura Niiharigun, 305, Ibaraki, Japan

    Koji Kuroda

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  1. Koji Kuroda
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Communicated by E. Lieb

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Kuroda, K. The geometrical phase transitions in a lattice model. Commun.Math. Phys. 80, 403–420 (1981). https://doi.org/10.1007/BF01208278

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  • DOI: https://doi.org/10.1007/BF01208278

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