Eur. Phys. J. B 33, 347-354 (2003)
https://doi.org/10.1140/epjb/e2003-00175-6

Universal properties of shortest paths in isotropically correlated random potentials

Theoretische Physik, Universität des Saarlandes, Postfach 15 11 50, 66041 Saarbrücken, Germany

Corresponding author: ^a schorr@lusi.uni-sb.de

Received: 20 December 2002
Revised: 10 April 2003
Published online: 20 June 2003

Abstract

We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d=2 and 3. We show that the exponent relation holds at least in d=2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations.