Replica Symmetry Breaking Instability in the 2D XY Model 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 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 unstable to RSB. The susceptibility χ associated to infinitesimal RSB perturbation in the high-temperature phase is found to diverge as χ ∝ (T − Tc) when T → T+ c . This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed. Typeset using REVTEX