Replica Symmetry Breaking Instability in the 2DXYModel in a Random Field

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 renormalization group 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 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.