Corner transfer matrix renormalization group method for two-dimensional self-avoiding walks and other O(n) models

Abstract

We present an extension of the corner transfer matrix renormalisation group (CTMRG) method to O(n) invariant models, with particular interest in the self-avoiding walk class of models (O(n=0)). The method is illustrated using an interacting self-avoiding walk model. Based on the efficiency and versatility when compared to other available numerical methods, we present CTMRG as the method of choice for two-dimensional self-avoiding walk problems.

4 pages 7 figures Substantial rewrite of previous version to include calculations of critical points and exponents. Final version accepted for publication in PRE (Rapid Communications)