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Peierls condition and number of ground states

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Abstract

Recently Pirogov and Sinai developped a theory of phase transitions in systems satisfying Peierls condition. We give a criterium for the Peierls condition to hold and apply it to several systems. In particular we prove that ferromagnetic system satisfies the Peierls condition iff its (internal) symmetry group is finite. And using an algebraic argument we show that in two dimensions the symmetry groups of reduced translation invariant systems is finite.

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References

  1. Bourbaki, N.: Algèbre commutative, Chapter 7 (§ 3, Theorem 2). Paris: Hermann 1965

    Google Scholar 

  2. Cassandro, M., Da Fano, A., Olivieri, E.: Commun. math. Phys.44, 45–51 (1975)

    Google Scholar 

  3. Dobrushin, R.L.: Funct. Anal. Applic.2, 302–312 (1968)

    Google Scholar 

  4. Gertsik, V.M.: Izv. Akad. Nauk. SSR, Ser. Mat.40, 448–462 (1976)

    Google Scholar 

  5. Gertsik, V.M., Dobrushin, R.L.: Funkts. Analiz.8, 12 (1974)

    Google Scholar 

  6. Holsztynski, W., Slawny, J.: Lett. Nuovo Cimento13, 534–538 (1975)

    Google Scholar 

  7. Holsztynski, W., Slawny, J.: Phase transitions in ferromagnetic spin systems at low temperatures. Preprint (1975)

  8. Pirogov, S.A.: Izv. Akad. Nauk SSR, Ser. Mat.39, 1404–1442 (1975)

    Google Scholar 

  9. Pirogov, S.A., Sinai, Ya.G.: Teor. Mat. Fiz.25, 358–369 (1975);26, 61–76 (1976)

    Google Scholar 

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

    Google Scholar 

  11. Slawny, J.: Commun. math. Phys.46, 75–97 (1976)

    Google Scholar 

  12. Wu, F.Y.: Phys. Rev. B4, 2312–2314 (1971)

    Google Scholar 

  13. Griffiths, R.B.: Phys. Rev. B7, 545–551 (1973)

    Google Scholar 

  14. Ruelle, D.: Formalisme thermodynamique. In: Séminaire Bourbaki 1974/75. Lecture notes in mathematics, Vol. 514. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

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Author notes

  1. J. Slawny

    Present address: Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

Authors and Affiliations

  1. Mathematics Department, The University of Western Ontario, London, Canada

    W. Holsztynski

  2. Institut de Physique Théorique, Université de Louvain, B-Louvain, Belgium

    J. Slawny

Authors
  1. W. Holsztynski
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  2. J. Slawny
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Communicated by E. Lieb

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Holsztynski, W., Slawny, J. Peierls condition and number of ground states. Commun.Math. Phys. 61, 177–190 (1978). https://doi.org/10.1007/BF01609493

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  • DOI: https://doi.org/10.1007/BF01609493

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