Application of polynomial algorithms to a random elastic medium

A randomly pinned elastic medium in two dimensions is modeled by a disorder ed fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimi zation. Dislocations are found to become unbound at large scale, and the el astic phase is thus unstable giving evidence for the absence of a Bragg gla ss in two dimensions. (C) 1999 Elsevier Science B.V. All rights reserved.