Boundary critical behavior ofd=2 self-avoiding walks on correlated and uncorrelated vacancies

Abstract

In this paper we present exact results for the critical exponents of interacting self-avoiding walks with ends at a linear boundary. Effective interactions are mediated by vacancies, correlated and uncorrelated, on the dual lattice. By choosing different boundary conditions, several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the $$\mathcal{O}(n = 1)$$ model. In particular, the problem of boundary exponents at the Θ′-point is fully solved, and implications forΘ-point universality are discussed. The surface crossover exponent at the special transition of noninteracting self-avoiding walks is also interpreted in terms of percolation dimensions.