Optimal path in weak and strong disorder

We generate optimal paths between two given sites on a lattice representing a disordered energy landscape by applying the Dijkstra algorithm. We study the geometrical and energetic scaling properties of the optimal path under two different energy distributions that yield the weak and strong disorder limits. Our numerical results, for both two and three dimensions, suggest that the optimal paths in weak disorder are in the same universality class as the directed polymers and in the strong disorder limit are fractals with exponents similar to that found by Cieplak et al. (Phys. Rev. Lett. 72 (1994) 2320; 76 (1996) 3754).