Ballistic behavior in a 1D weakly self-avoiding walk with decaying energy penalty

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Abstract

We consider a weakly self-avoiding walk in one dimension in which the penalty for visiting a site twice decays as exp[-β|t-s|-p] where t and s are the times at which the common site is visited and p is a parameter. We prove that if p<1 and β is sufficiently large, then the walk behaves ballistically, i.e., the distance to the end of the walk grows linearly with the number of steps in the walk. We also give a heuristic argument that if p>3/2, then the walk should have diffusive behavior. The proof and the heuristic argument make use of a real-space renormalization group transformation.

Original languageEnglish (US)
Pages (from-to)565-579
Number of pages15
JournalJournal of Statistical Physics
Volume77
Issue number3-4
DOIs
StatePublished - Nov 1 1994

Keywords

  • Weakly self-avoiding walk
  • ballistic

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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