Minimal knotted polygons in cubic lattices

TL;DR

This paper uses BFACF algorithms to analyze minimal length knotted polygons in cubic lattices, focusing on their statistics, entropy, curvature, and writhe.

Contribution

It introduces a method to estimate properties of minimal knotted polygons across different cubic lattices using specialized algorithms.

Findings

Estimated statistics and writhe of minimal knotted polygons

Analyzed entropy and lattice curvature of these polygons

Compared properties across simple, face centered, and body centered cubic lattices

Abstract

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe.