A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

TL;DR

This paper introduces a more efficient transfer-matrix algorithm for exact enumeration of self-avoiding polygons on the square lattice, significantly extending enumeration length and outperforming previous methods.

Contribution

A novel transfer-matrix algorithm that improves efficiency and extends enumeration capabilities for self-avoiding polygons on the square lattice.

Findings

Enumeration length extended to 130 from 110

Significant reduction in running time

Outperforms previous algorithms

Abstract

We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.