Walks, trials and polymers with loops

Y. Shapir, Y. Oono

Research output: Contribution to journalArticlepeer-review


Lattice models interpolating between free and self-avoiding random walks are investigated. Generating functions are constructed for k-tolerant walks, various trail problems, etc. For trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc=4. Their asymptotic large-scale behaviours are the same as those of the self-avoiding walk. Arguments are presented to support the same conclusion for much more general classes of walks including k-tolerant walks. One of the models exhibits a new tricritical point of order epsilon 1/2 if the fugacity for crossing is increased.

Original languageEnglish (US)
Article number003
Pages (from-to)L39-L44
JournalJournal of Physics A: Mathematical and General
Issue number2
StatePublished - 1984
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


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