English

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

Statistical Mechanics 2007-05-23 v1

Abstract

The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\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.

Keywords

Cite

@article{arxiv.cond-mat/0106627,
  title  = {Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk},
  author = {L. Turban},
  journal= {arXiv preprint arXiv:cond-mat/0106627},
  year   = {2007}
}

Comments

Old paper, for archiving. 8 pages, 1 figure, epsf, IOP macro