Critical behaviour at an edge for the SAW and Ising model

Abstract

The authors have studied the behaviour of two- and three-dimensional self avoiding walks confined to a wedge of wedge angle alpha . Series have been obtained and analysed for the (angular dependent) critical exponents characterising various edge susceptibilities. In terms of a general scaling form for the edge free energy, fe approximately t(d-2) nu psi e(ht-y0 nu, h1t-y1 nu, h 2t-y2 nu), they find for the two-dimensional case the following scaling indices: y0=91/48, y1=3/8, y2( alpha )=-5 pi /8 alpha . They argue that these results are exact, from which follow all exponents for the bulk, surface and edge problem. In three dimensions the authors obtain y0 approximately=2.488, y1=0.65+or-0.02..