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Kac Polymers

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Abstract

We show how a polymer in two dimensions with a self-repelling interaction of Kac type exhibits a diffusive–ballistic transition if considered on the appropriate scale.

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References

  1. R Hofstad Particlevan der F den Hollander W König (1997) ArticleTitleCentral limit theorem for a weakly interacting random polymer Markov Process. Rel. Fields 3 1–62

    Google Scholar 

  2. D Brydges T Spencer (1985) ArticleTitleSelf avoiding walk in 5 or more dimensions Commun. Math. Phys. 97 125–148 Occurrence Handle10.1007/BF01206182

    Article  Google Scholar 

  3. R vander Hofstad F den Hollander G Slade (1998) ArticleTitleA new inductive approach to the lace expansion for self-avoiding walks Probab. Theory Rel. Fields 111 253–286 Occurrence Handle10.1007/s004400050168

    Article  Google Scholar 

  4. N Madrasand G Slade (1993) The Self-Avoiding Walk. Probability and its Applications line break. Birkhauser Boston, Inc. Boston, MA

    Google Scholar 

  5. R vander Hofstad (2001) ArticleTitleThe lace expansion approach to ballistic behaviour for one-dimensional weakly self-avoiding walks Probab. Theory Rel. Fields 119 311–349

    Google Scholar 

  6. D Iagolitzer J Magnen (1994) ArticleTitlePolymers in a weak random potential in dimension four: rigorous renormalization group analysis Commun. Math. Phys. 162 85–121

    Google Scholar 

  7. R. L. Dobrushin (1973) ArticleTitleAnalyticity of correlation functions in one-dimensional classical systems with slowly decreasing potentials Commun. Math. Phys. 32 269–289 Occurrence Handle10.1007/BF01645609

    Article  Google Scholar 

  8. M Cassandro E Olivieri (1981) ArticleTitleRenormalization group and analyticity in one dimension: a proof of Dobrushin’s theorem Commun. Math. Phys. 80 255–269 Occurrence Handle10.1007/BF01213013

    Article  Google Scholar 

  9. M Cassandro E Orlandi E Presutti (1993) ArticleTitleInterfaces and typical Gibbs configurations for one-dimensional Kac potentials Probab. Theory Rel. Fields 96 57–96 Occurrence Handle10.1007/BF01195883

    Article  Google Scholar 

  10. P Buttà P Picco (1998) ArticleTitleLarge deviation principle for one dimensional vector spin models with Kac potentials J. Stat. Phys. 92 101–150 Occurrence Handle10.1023/A:1023095619236

    Article  Google Scholar 

  11. J Fròhlich T Spencer (1982) ArticleTitleThe phase transition in the one-dimensional Ising model with 1/r2 interaction energy Commun. Math. Phys. 84 87–101 Occurrence Handle10.1007/BF01208373

    Article  Google Scholar 

  12. R. L. Dobrushin (1970) ArticleTitlePrescribing a system of random variables by conditional distributions Theory Probab. Appl. 15 458–486 Occurrence Handle10.1137/1115049

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma ‘LaSapienza’, P.le Aldo Moro 2, 00185, Roma, Italy

    Paolo Buttà

  2. Departamento de Matemàtica, Universida de Federal de Minas Gerais, 30161-970, Belo Horizonte, MG, Brazil

    Aldo Procacci

  3. Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, Via della Ricerca Scientifica, 00133, Roma, Italy

    Benedetto Scoppola

Authors
  1. Paolo Buttà
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  2. Aldo Procacci
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  3. Benedetto Scoppola
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Correspondence to Paolo Buttà.

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Buttà, P., Procacci, A. & Scoppola, B. Kac Polymers. J Stat Phys 119, 643–658 (2005). https://doi.org/10.1007/s10955-005-3771-0

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  • DOI: https://doi.org/10.1007/s10955-005-3771-0

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