A randomly pinned elastic medium in two dimensions is modeled by a disorder
ed fully packed loop (FPL) model. The energetics of disorder-induced disloc
ations is studied using exact and polynomial algorithms from combinatorial
optimization. Dislocations are found to become unbound at large scale, and
the elastic phase is, thus, unstable giving evidence for the absence of a B
ragg glass in two dimensions. (C) 2000 Elsevier Science B.V. All rights res
erved.