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On the Surface Pressure for the Edwards-Anderson Model

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Abstract

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) τ∂Λ in terms of a quenched moment of the bond-overlap on the surface. We consider free Φ, periodic Π and antiperiodic Π* boundary conditions (by symmetry τ(Π) ∂Λ=τ(Π*) ∂Λ), and prove the bounds We show moreover that at high temperatures τ(Φ) ∂Λ is close to β2/4 and τ(Π) ∂Λ is close to β2/4 uniformly in the volume Λ.

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References

  1. Berretti, A.: J. Stat. Phys. 38(3/4), 483–496 (1985)

    Google Scholar 

  2. von Dreifus, H., Klein, A., Perez, J.F.: Commun. Math. Phys. 170, 21–39 (1995)

    MATH  Google Scholar 

  3. Contucci, P., Graffi, S.: J. Stat. Phys. 115(1/2), 581–589 (2004)

    Google Scholar 

  4. Contucci, P., Degli Esposti, M., Giardinà, C., Graffi, S.: Commun. Math. Phys. 236, 55–63 (2003)

    MATH  Google Scholar 

  5. van Enter, A.C.D., van Hemmen, J.L.: J. Stat. Phys. 32, 141–152 (1983)

    Google Scholar 

  6. Fisher, M.E., Caginalp, G.: Commun. Math. Phys. 56(1), 11–56 (1977)

    Google Scholar 

  7. Fisher, D.S., Huse, D.H.: Phys. Rev. Lett. 56, 1601 (1986)

    Article  Google Scholar 

  8. Fröhlich, J., Imbrie, J.Z.: Commun. Math. Phys. 96, 145–180 (1984)

    MathSciNet  Google Scholar 

  9. Fisher, M., Lebowitz, J.: Commun. Math. Phys. 19, 251–272 (1970)

    Google Scholar 

  10. Guerra, F.: Phys. Rev. Lett. 28(18), 1213–1215 (1972)

    Article  Google Scholar 

  11. Griffiths, R.B.: Phys. Rev. Lett. 23, 17 (1969)

    Article  Google Scholar 

  12. Guerra, F., Rosen, L., Simon, B.: Ann. Inst. H. Poincare A25(3), 231–334 (1976)

    Google Scholar 

  13. Guerra, F., Toninelli, F.: Commun. Math. Phys. 230, 71–79 (2002)

    MATH  Google Scholar 

  14. Mezard, M., Parisi, G., Virasoro, M.A.: Spin Glass theory and beyond. Singapore: World Scien., 1987

  15. Newmnan, C.M., Stein, D.L.: http://arxiv.org/abs/cond-mat/0301403, 2003

  16. Simon, B.: The statistical mechanics of lattice gases. Princeton, NJ: Princeton Univ. Press. 1992

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, 40127, Bologna, Italy

    Pierluigi Contucci & Sandro Graffi

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  1. Pierluigi Contucci
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  2. Sandro Graffi
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Correspondence to Pierluigi Contucci.

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Communicated by M. Aizenman

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Contucci, P., Graffi, S. On the Surface Pressure for the Edwards-Anderson Model. Commun. Math. Phys. 248, 207–216 (2004). https://doi.org/10.1007/s00220-004-1094-7

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  • DOI: https://doi.org/10.1007/s00220-004-1094-7

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