Scaling Properties of Weakly Self-Avoiding Fractional Brownian Motion in One Dimension

TL;DR

This paper investigates the scaling behavior of weakly self-avoiding fractional Brownian motion in one dimension using numerical methods, confirming a mean field formula for the Flory index.

Contribution

It introduces an off-lattice discretization and applies a Metropolis algorithm to analyze the asymptotic scaling, validating a theoretical Flory index for this model.

Findings

Good agreement with the Flory index prediction

Numerical evidence supporting the mean field formula

Extension of fractional Brownian motion analysis to self-avoiding cases

Abstract

We use an off-lattice discretization of fractional Brownian motion and a Metropolis Algorithm to determine the asymptotic scaling of this discretized fractional Brownian motion under the influence of an excluded volume as in the Edwards and Domb-Joyce models. We find a good agreement between the Flory index describing the scaling of end-to-end length with a mean field formula proposed earlier for this class of models.