Interaction Versus Entropic Repulsion for Low Temperature Ising Polymers View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-03

AUTHORS

Dmitry Ioffe, Senya Shlosman, Fabio Lucio Toninelli

ABSTRACT

Contours associated to many interesting low-temperature statistical mechanics models (2D Ising model, (2+1)D SOS interface model, etc) can be described as self-interacting and self-avoiding walks on Z2. When the model is defined in a finite box, the presence of the boundary induces an interaction, that can turn out to be attractive, between the contour and the boundary of the box. On the other hand, the contour cannot cross the boundary, so it feels entropic repulsion from it. In various situations of interest (in Caputo et al. Ann. Probab., arXiv:1205.6884, J. Eur. Math. Soc., arXiv:1302.6941, arXiv:1406.1206, Ioffe and Shlosman, in preparation), a crucial technical problem is to prove that entropic repulsion prevails over the pinning interaction: in particular, the contour-boundary interaction should not modify significantly the contour partition function and the related surface tension should be unchanged. Here we prove that this is indeed the case, at least at sufficiently low temperature, in a quite general framework that applies in particular to the models of interest mentioned above. More... »

PAGES

1007-1050

References to SciGraph publications

  • 2015-06. An Invariance Principle to Ferrari–Spohn Diffusions in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2002-02. Surface Tension and the Ornstein–Zernike Behaviour for the 2D Blume–Capel Model in JOURNAL OF STATISTICAL PHYSICS
  • 1996-06. Constrained variational problem with applications to the Ising model in JOURNAL OF STATISTICAL PHYSICS
  • 1999-07. Interface, Surface Tension and Reentrant Pinning Transition in the 2D Ising Model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1999-01. “Non-Gibbsian” States and their Gibbs Description in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1991. Gibbs Random Fields, Cluster Expansions in NONE
  • 2015-12. On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature in PROBABILITY THEORY AND RELATED FIELDS
  • 2003-03. Ornstein-Zernike theory for finite range Ising models above Tc in PROBABILITY THEORY AND RELATED FIELDS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-014-1153-1

    DOI

    http://dx.doi.org/10.1007/s10955-014-1153-1

    DIMENSIONS

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