The persistence length of two dimensional self avoiding random walks

TL;DR

This paper investigates how directional correlations decay in two-dimensional self-avoiding random walks, showing that the persistence length is finite due to a decay faster than 1/j, based on enumeration and Monte Carlo methods.

Contribution

It provides evidence that the persistence length of 2D self-avoiding walks is finite, using exact enumeration and Monte Carlo simulations to analyze correlation decay.

Findings

Directional correlations decay faster than 1/j

Persistence length of the walk is finite

Monte Carlo and enumeration support the decay rate

Abstract

The decay of directional correlations in self-avoiding random walks on the square lattice is investigated. Analysis of exact enumerations and Monte Carlo data suggest that the correlation between the directions of the first step and the j-th step of the walk decays faster than 1/j, indicating that the persistence length of the walk is finite.