Transfer matrix algorithm for computing the exact partition function of a square lattice polymer

TL;DR

This paper introduces a transfer matrix algorithm that efficiently computes the exact partition function of square lattice polymers, significantly reducing computation time compared to explicit enumeration for chains longer than 25 units.

Contribution

The paper extends a previous algorithm to compute the exact partition function of square lattice polymers, achieving faster calculations for longer chains.

Findings

Computation time scales as approximately 1.6^N, faster than the 2.7^N scaling of explicit enumeration.

Exact partition functions for polymers up to length N=42 are obtained.

Transfer matrix method outperforms explicit enumeration for N>25.

Abstract

I develop a transfer matrix algorithm for computing the exact partition function of a square lattice polymer with nearest-neighbor interaction, by extending a previous algorithm for computing the total number of self-avoiding walks. The computation time scales as ~1.6^N with the chain length N, in contrast to the explicit enumeration where the scaling is ~ 2.7^N. The exact partition function can be obtained faster with the transfer matrix method than with the explicit enumeration, for N>25. The new results for up to N=42 are presented.