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

TL;DR

This paper investigates the instability of the replica symmetric solution in the 2D XY model with a random field, demonstrating that replica symmetry breaking occurs and diverges near the critical temperature, indicating RSB in finite dimensions.

Contribution

It constructs RG recursion relations allowing for RSB analysis and shows the instability of the known glass phase fixed point in the 2D XY model with a random field.

Findings

RSB fixed point is unstable in the glass phase.

Susceptibility diverges as temperature approaches critical from above.

Provides analytical evidence for RSB in finite-dimensional models.

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 $T \rightarrow T_c^{+}$. This provides analytical evidence that RSB occurs in finite dimensional models. The physical consequences for the glass phase are discussed.