Probability distributions of line lattices in random media from the 1D Bose gas

The statistical properties of a two-dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel map ping of the dilute random Line lattice onto the weak coupling limit of a pu re Bose gas with delta-function interactions. Using this mapping, we calcul ate the cumulants of the free energy in the dilute limit exactly. The relat ion between density and displacement correlation functions in the two model s is examined and compared with existing results from renormalization group and variational ansatze. (C) 2001 Published by Elsevier Science B,V.