We study the 2D vortex-free XY model in a random field, a model for randomly
pinned flux lines in a plane. We construct controlled RG recursion relations
which allow for replica symmetry breaking (RSB). The fixed point previously
found by Cardy and Ostlund in the glass phase T<Tc is {\it unstable} to RSB.
The susceptibility χ associated to infinitesimal RSB perturbation in the
high-temperature phase is found to diverge as χ∝(T−Tc)−γ
when T→Tc+. This provides analytical evidence that RSB occurs
in finite dimensional models. The physical consequences for the glass phase are
discussed.Comment: 8 pages, REVTeX, LPTENS-94/2