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Journal of Statistical Physics

, Volume 77, Issue 3–4, pp 565–579 | Cite as

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

  • Tom Kennedy
Articles

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 ] wheret ands are the times at which the common site is visited andp is a parameter. We prove that ifp<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 ifp>3/2, then the walk should have diffusive behavior. The proof and the heuristic argument make use of a real-space renormalization group transformation.

Key Words

Weakly self-avoiding walk ballistic 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Tom Kennedy
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucson

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