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Cluster expansion ford-dimensional lattice systems and finite-volume factorization properties

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Abstract

We consider classical lattice systems with finite-range interactions ind dimensions. By means of a block-decimation procedure, we transform our original system into a polymer system whose activity is small provided a suitable factorization property of finite-volume partition functions holds. In this way we extend a result of Olivieri.

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References

  1. E. Olivieri, On a cluster expansion from lattice spin systems: A finite size condition for the convergence,J. Stat. Phys. 50:1179 (1988).

    Google Scholar 

  2. G. Gallavotti and S. Miracle-Sole, Correlation function of a lattice system,Commun. Math. Phys. 7:274 (1968).

    Google Scholar 

  3. R. L. Dobrushin and S. B. Shlosman, Constructive criterion for the uniqueness of Gibbs field, inStatistical Physics and Dynamical Systems, D. Sasz and D. Petz, eds. (Birkäuser, Boston, 1985).

    Google Scholar 

  4. R. L. Dobrushin and S. B. Shlosman, Completely analytical Gibbs fields, inStatistical Physics and Dynamical Systems, D. Sasz and D. Petz, eds. (Birkäuser, Boston, 1985).

    Google Scholar 

  5. R. L. Dobrushin, Induction on volume and no cluster expansion, inProceedings of the VIIth IAMP, Marseille '86, M. Mebkhout and R. Sénéor, eds. (World Scientific, Singapore, 1987).

    Google Scholar 

  6. R. L. Dobrushin and S. B. Shlosman, Completely analytical interactions: A constructive description,J. Stat. Phys. 46:983 (1987).

    Google Scholar 

  7. M. Cassandro and E. Olivieri, Renormalization group and analyticity in one dimension: a Proof of Dobrushin's theorem,Commun. Math. Phys. 80:255 (1981).

    Google Scholar 

  8. M. Campanino, M. Capocaccia, and E. Olivieri, Analyticity for one dimensional systems with long range superstable interactions,J. Stat. Phys. 33:437 (1983).

    Google Scholar 

  9. G. Gallavotti, A. Martin Löf, and S. Miracle-Sole, Some problems connected with the description of coexisting phases at low temperatures in the Ising model, inLecture Notes in Physics, Vol. 20, pp. 162–204.

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Author notes

  1. Enzo Olivieri

    Present address: Dipartimento di Matematica, Universitá dell'Aquila, L'Aquila, Italy

Authors and Affiliations

  1. Centre de Physique Théorique, Marseille, France

    Enzo Olivieri & Pierre Picco

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  1. Enzo Olivieri
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  2. Pierre Picco
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Olivieri, E., Picco, P. Cluster expansion ford-dimensional lattice systems and finite-volume factorization properties. J Stat Phys 59, 221–256 (1990). https://doi.org/10.1007/BF01015569

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  • DOI: https://doi.org/10.1007/BF01015569

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