Interaction Versus Entropic Repulsion for Low Temperature Ising Polymers

Dmitry Ioffe, Senya Shlosman, Fabio Lucio Toninelli

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 (Formula presented.). 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.

Original languageEnglish
Pages (from-to)1007-1050
Number of pages44
JournalJournal of Statistical Physics
Volume158
Issue number5
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Cluster expansion
  • Entropic repulsion
  • Ising model
  • SOS model

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