DIRECTED WALK IN RANDOM-MEDIA

Directed walk in random media is described by both extensive simulations and the creak noise expansion. The energy fluctuation Delta E of the lowest energy E grows as t(omega) with omega approximate to 1/(d+1). We find that the probability distribution P(a)da of the normalized energy a=(E-[E])/Delta E is independent of the models. In dimension d=2+1, both the high temperature expansion and the measurement of the third cumulant of P(a) support that there is no finite temperature phase transition. Instead, the crossover length t* is very large at high temperature and has been found to vary as In t*similar to T-2. The generalization of real random potential to complex random potential is also discussed.