Replica Symmetry Breaking Instability in the 2D XY model in a random field

Abstract

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 $T<T_c$ is {\it unstable} to RSB. The susceptibility $\chi$ associated to infinitesimal RSB perturbation in the high-temperature phase is found to diverge as $\chi \propto (T-T_c{)}^{-\gamma }$ when $T\to T_c^{+}$. This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed.

8 pages, REVTeX, LPTENS-94/27

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