Optimal Path in Two and Three Dimensions

Details Optimal Path in Two and Three Dimensions Optimal Path in Two and Three Dimensions

1999-04-13

arxiv.org/abs/cond-mat/9904176v1

Phys. Rev. E 58, 7642 (1998)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures

Scientific paper

10.1103/PhysRevE.58.7642

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.

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