A note on mean-field behavior for self-avoiding walk on branching planes

Research output: Contribution to journalArticle

Abstract

We consider the critical behavior of the susceptibility of the self-avoiding walk on the graph T×Z, where T is a Bethe lattice with degree k and Z is the one dimensional lattice. By directly estimating the two-point function using a method of Grimmett and Newman, we show that the bubble condition is satisfied when k>2, and therefore the critical exponent associated with the susceptibility equals 1.

Original languageEnglish (US)
Pages (from-to)673-680
Number of pages8
JournalJournal of Statistical Physics
Volume81
Issue number3-4
DOIs
StatePublished - Nov 1 1995

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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