Stability of the Bragg glass phase in a layered geometry

We study the stability of the dislocation-free Bragg glass phase in a layered geometry consisting of coupled parallel planes of d = 1 + 1 vortex lines lying within each plane, in the presence of impurity disorder. Using renormalization group, replica variational calculations and physical arguments, we find that at temperatures T < T-G the 3D Bragg glass phase is always stable for weak disorder. It undergoes a weakly first-order transition into a decoupled 2D vortex glass upon increase of disorder.