Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
Abstract
The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x= Ctα. 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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