Honeycomb lattice polygons and walks as a test of series analysis techniques

TL;DR

This paper computes extensive series expansions for self-avoiding walks and polygons on the honeycomb lattice, providing precise estimates of critical parameters that align well with theoretical predictions.

Contribution

It introduces comprehensive series data for honeycomb lattice walks and polygons, enabling accurate testing of series analysis techniques against theoretical expectations.

Findings

Accurate estimates of the connective constant and critical exponents.

Series analysis results agree with theoretical predictions.

Provides metric properties and area-distribution moments for polygons.

Abstract

We have calculated long series expansions for self-avoiding walks and polygons on the honeycomb lattice, including series for metric properties such as mean-squared radius of gyration as well as series for moments of the area-distribution for polygons. Analysis of the series yields accurate estimates for the connective constant, critical exponents and amplitudes of honeycomb self-avoiding walks and polygons. The results from the numerical analysis agree to a high degree of accuracy with theoretical predictions for these quantities.