A NOTE ON MEAN-FIELD BEHAVIOR FOR SELF-AVOIDING WALK ON BRANCHING PLANES

Authors
WU CC
Citation
Cc. Wu, A NOTE ON MEAN-FIELD BEHAVIOR FOR SELF-AVOIDING WALK ON BRANCHING PLANES, Journal of statistical physics, 81(3-4), 1995, pp. 673-680
Citations number
13
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Journal of statistical physics → ACNP
ISSN journal
00224715
Volume
81
Issue
3-4
Year of publication
1995
Pages
673 - 680
Database
ISI
SICI code
0022-4715(1995)81:3-4<673:ANOMBF>2.0.ZU;2-R
Abstract
We consider the critical behavior of the susceptibility of the self-av oiding walk on the graph T x Z, where T is a Bethe lattice with degree k and Z is the one dimensional lattice. By directly estimating the tw o-point function using a method of Grimmett and Newman, we show that t he bubble condition is satisfied when k > 2, and therefore the critica l exponent associated with the susceptibility equals 1.