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On the absence of breakdown of symmetry for the plane rotator model with long range unbounded random interaction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1109)

Abstract

We study the plane rotator model with Hamiltonian \(- \frac{1}{2}\sum\limits_{x \ne y} {\frac{{Jxy\cos (\mathcal{O}_x - \mathcal{O}_y )}}{{\left| {x - y} \right|^{3 + \mathcal{E}} }}}\)where Jxy for different pair (x.y) are independent symmetric unbounded random variables. It is proved that for almost all J, all Gibbs states P(J) are invariant by rotation.

Keywords

  • Long Range
  • Spin Glass
  • Relative Entropy
  • Gibbs State
  • Borel Cantelli Lemma

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References

  1. S.F. EDWARDS and P.W. ANDERSON, J. Phys. F 5, 965 (1975).

    CrossRef  Google Scholar 

  2. A.C.D. VAN ENTER and R.B. GRIFFITHS, Comm.Math.Phys. 90, 319 (1983).

    CrossRef  MathSciNet  Google Scholar 

  3. P.A. VUILLERMOT, J. Phys. A10, 1319 (1977).

    MathSciNet  Google Scholar 

  4. K.M. KHANIN and Ya. G. SINAI, J. Stat. Phys. 20, 573 (1979).

    CrossRef  MathSciNet  Google Scholar 

  5. A.C.D. VAN ENTER and J.L. VAN HEMMEN, J. Stat. Phys. 32, 141 (1983).

    CrossRef  Google Scholar 

  6. K.M. KHANIN, Theoretich i Matem Fiz., 43, 253 (1980).

    MathSciNet  Google Scholar 

  7. M. CASSANDRO, E. OLIVIERI, B. TIROZZI, Comm.Math.Phys. 87, 229 (1982).

    CrossRef  MathSciNet  Google Scholar 

  8. P. PICCO, J. Stat. Phys. 32, 627 (1983).

    CrossRef  MathSciNet  Google Scholar 

  9. P. PICCO, Upper bound on the decay of correlations in the plane rotator model with long range random interaction, Preprint Marseille (1982).

    Google Scholar 

  10. C. PFISTER, Comm.Math.Phys. 79, 181 (1981).

    CrossRef  MathSciNet  Google Scholar 

  11. C. PFISTER and J. FROHLICH, Comm.Math.Phys. 81, 277 (1981).

    CrossRef  MathSciNet  Google Scholar 

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© 1985 Springer-Verlag

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Picco, P. (1985). On the absence of breakdown of symmetry for the plane rotator model with long range unbounded random interaction. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Aspects of Classical and Quantum Systems. Lecture Notes in Mathematics, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101542

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  • DOI: https://doi.org/10.1007/BFb0101542

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13914-0

  • Online ISBN: 978-3-540-39138-8

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