Optimal Path in Two and Three Dimensions

TL;DR

This paper investigates the properties of optimal paths in disordered energy landscapes using Dijkstra's algorithm, revealing their universality class and relevance to physical polymer systems in two and three dimensions.

Contribution

It demonstrates that optimal paths in random energy landscapes belong to the same universality class as directed polymers, supported by numerical analysis in 2D and 3D.

Findings

Optimal paths follow the universality class of directed polymers.

Numerical results confirm scaling properties in 2D and 3D.

Relevance to physical polymer systems in disordered landscapes.

Abstract

We apply the Dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape. We study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution. Our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers. We present physical realizations of polymers in disordered energy landscape for which this result is relevant.