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

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Self-avoiding Walk
Mean Field
Susceptibility
Branching
magnetic permeability
Bethe Lattice
Critical Behavior
Critical Exponents
Bubble
estimating
bubbles
exponents
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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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.",
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A note on mean-field behavior for self-avoiding walk on branching planes. / Wu, C. Chris.

In: Journal of Statistical Physics, Vol. 81, No. 3-4, 01.11.1995, p. 673-680.

Research output: Contribution to journalArticle

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