Universality of neighbour-avoiding and self-avoiding walks on the square lattice

Abstract

It is shown that, within position-space renormalisation group (PSRG) theory, neighbour-avoiding walks (NAWs) and self-avoiding walks (SAWs) on the square lattice obey the same 'end-to-end distance' critical exponent nu . This universality is shown by applying a recent finite lattice renormalisation transformation to ordinary and oriented NAW and SAW problems and then using an exact equivalence between SAWs on an oriented lattice and NAWs on its covering lattice. The universality class includes several oriented walk problems.