2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17950The 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.Old paper, for archiving. 8 pages, 1 figure, epsf, IOP macroStatistical Mechanicstext