Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk

2001/06/29 by L. Turban
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/25/3/008

published as J. Phys. A 25 (1992) L127 · Old paper, for archiving. 8 pages, 1 figure, epsf, IOP macro

arxiv created 2001/06/29 · arxiv updated 2009/11/30

Abstract

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=± Ct^α. Using a scaling argument, 1/C is shown to be a marginal variable when α=ν_⊥/ν_∥=1/2, i.e., on a parabola. As a consequence the directed walk may display varying local exponents. Such a behaviour is indeed observed for restricted walks. This generalizes a result of Cardy showing that nonuniversal behaviour occurs at corners for isotropic systems.

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