Three-dimensional terminally attached self-avoiding walks and bridges

TL;DR

This paper investigates the properties of three-dimensional terminally attached self-avoiding walks and bridges on a cubic lattice, using series analysis and Monte Carlo simulations to explore their scaling relations and universal amplitude ratios.

Contribution

It provides numerical evidence for a scaling relation and proposes that a certain amplitude ratio is a universal quantity in these models.

Findings

Strong numerical evidence for a scaling relation.

Identification of a universal amplitude ratio.

Support for the connection between self-avoiding walks and bridges.

Abstract

We study terminally attached self-avoiding walks and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide strong numerical evidence supporting a scaling relation between self-avoiding walks, bridges, and terminally attached self-avoiding walks, and posit that a corresponding amplitude ratio is a universal quantity.