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

TL;DR

This paper extends the corner transfer matrix renormalization group method to O(n) models, especially self-avoiding walks, demonstrating its efficiency and versatility as a numerical tool for 2D self-avoiding walk problems.

Contribution

The paper introduces an extension of CTMRG to O(n) models, providing a powerful numerical approach for 2D self-avoiding walks and related models.

Findings

CTMRG is efficient for 2D self-avoiding walks.

The method outperforms other numerical techniques.

It is versatile for various 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.