A parallel algorithm for the enumeration of self-avoiding polygons on the square lattice

TL;DR

This paper presents a parallel algorithm for enumerating self-avoiding polygons on a square lattice, extending series data and providing precise estimates of critical parameters and universal amplitude combinations.

Contribution

The authors developed a parallel enumeration algorithm that significantly extends series data for self-avoiding polygons and improves estimates of critical parameters.

Findings

Enumerated polygons up to perimeter length 110.

Extended series for area-weighted moments and radius of gyration to 100.

Provided highly accurate estimates of the connective constant and critical exponent.

Abstract

We have developed a parallel algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 110. We have also extended the series for the first 10 area-weighted moments and the radius of gyration to 100. Analysis of the resulting series yields very accurate estimates of the connective constant $\mu =2.63815853031(3)$ (biased) and the critical exponent $\alpha = 0.5000001(2)$ (unbiased). In addition we obtain very accurate estimates for the leading amplitudes confirming to a high degree of accuracy various predictions for universal amplitude combinations.