Interference of directed paths in disordered systems.

Abstract

We consider sums over directed paths, interfering due to quenched random elements controlling either the phase or the sign of each term. The former enter the determination of electronic transport in the localized regime, and the latter that of correlations in the high-temperature phase of the Ising spin-glass. Numerical computations in two dimensions indicate anomalous fluctuations dominated by untypical paths, with scaling behavior similar to that of random but positive impurities. This is argued to follow from a bound state, due to a subtle attraction between pairs, in replica space.