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Decay of correlations for infinite range interactions in unbounded spin systems

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Abstract

In unbounded spin systems at high temperature with two-body potential we prove, using the associated polymer model, that the two-point truncated correlation function decays exponentially (respectively with a power law) if the potential decays exponentially (respectively with a power law). We also give a new proof of the convergence of the Mayer series for the general polymer model.

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References

  1. Kunz, H.: Analiticity and clustering properties of unbounded spin systems. Commun. Math. Phys.59, 53–69 (1978)

    Google Scholar 

  2. Israel, R.B., Nappi, C.R.: Exponential clustering for long-range integer spin systems. Commun. Math. Phys.68, 29–37 (1979)

    Google Scholar 

  3. Gross, L.: Decay of correlations in classical lattice models at high temperature. Commun. Math. Phys.68, 9–27 (1979)

    Google Scholar 

  4. Duneau, M., Souillard, B.: Cluster properties of lattice and continuous systems. Commun. Math. Phys.47, 155–166 (1976)

    Google Scholar 

  5. Gruber, C., Kunz, H.: General properties of polymer systems. Commun. Math. Phys.22, 133–161 (1971)

    Google Scholar 

  6. Gallavotti, G., Martin-Löf, A., Miracle-Solé, S.: Some problems connected with the description of cohexisting phases at low temperature in the Ising model. In: Lecture Notes in Physics, Vol. 20, pp. 162–202. Berlin, Heidelberg, New York: Springer 1971

    Google Scholar 

  7. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969

    Google Scholar 

  8. Campanino, M., Capocaccia, D., Tirozzi, B.: The local central limit theorem for a Gibbs random field. Commun. Math. Phys.70, 125–132 (1979)

    Google Scholar 

  9. Cassandro, M., Olivieri, E.: Renormalization group and analiticity in one dimension: A proof of the Dobrushin's Theorem. Commun. Math. Phys.80, 255–269 (1981)

    Google Scholar 

  10. Penrose, O.: Convergence of fugacity expansions for classical systems. In: Statistical mechanics: foundations and applications, Bak, A. (ed.). New York: Benjamin 1967

    Google Scholar 

  11. Brydges, D., Federbush, P.: A new form of the Mayer expansion in classical statistical mechanics. J. Math. Phys.19, 2064–2067 (1978)

    Google Scholar 

  12. Moon, J.W.: Enumerating labelled trees. In: Graph theory and theoretical physics, Harary, F. (ed.). New York: Academic Press 1967

    Google Scholar 

  13. Rota, G.C.: Z. Wahrscheinlichkeitstheorie Verw. Gebiete2, 340 (1964)

    Google Scholar 

  14. Malyshev, V.A.: Uniform cluster estimates for lattice models. Commun. Math. Phys.64, 131–157 (1979)

    Google Scholar 

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Authors and Affiliations

  1. Istituto di Matematica, Università di Roma, C.N.R. (G.N.F.M.), I-00185, Roma, Italy

    Camillo Cammarota

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  1. Camillo Cammarota
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Communicated by E. Lieb

Supported by C.N.R. (G.N.F.M.)

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Cammarota, C. Decay of correlations for infinite range interactions in unbounded spin systems. Commun.Math. Phys. 85, 517–528 (1982). https://doi.org/10.1007/BF01403502

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  • DOI: https://doi.org/10.1007/BF01403502

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