Random Walks with Long-Range Self-Repulsion on Proper Time

TL;DR

This paper introduces a self-repelling random walk model with long-range interactions decreasing as a power law, providing analytic results for the scaling exponent and validating them through Monte Carlo simulations.

Contribution

It presents a novel model of self-repelling walks with long-range interactions and derives analytic exponents, supported by numerical simulations.

Findings

Analytic exponent $ u$ matches Monte Carlo results

Long-range self-repulsion affects scaling behavior

Efficient algorithms for simulation are analyzed

Abstract

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.