Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas

Details Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas

2001-01-16

arxiv.org/abs/cond-mat/0101247v1

Physics

Condensed Matter

Statistical Mechanics

38 pages, 2 figures

Scientific paper

10.1016/S0550-3213(01)00102-X

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 mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas with delta-function interactions. Using this mapping, we calculate the cumulants of the free energy in the dilute limit exactly. The relation between density and displacement correlation functions in the two models is examined and compared with existing results from renormalization group and variational ansaetze.

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