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

L. Turban
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Abstract

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^α. Using a scaling argument, 1/C is shown to be a marginal variable when α=ν_\perp/ν_\parallel=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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L. Turban. 2001-06-29. Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk. https://doi.org/10.1088/0305-4470%2F25%2F3%2F008

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