Stability of Elastic Glass Phases in Random FieldXYMagnets and Vortex Lattices in Type-II Superconductors

A description of a dislocation-free elastic glass phase in terms of domain walls is developed and used as the basis of a renormalization group analysis of the energetics of dislocation loops added to the system. It is found that even after optimizing over possible paths of large dislocation loops, their energy is still very likely to be positive when the dislocation core energy is large. This implies the existence of an equilibrium elastic glass phase in three-dimensional random field $\mathrm{XY}$ magnets, and a dislocation-free, bond orientationally ordered “Bragg glass” phase of vortices in dirty type-II superconductors.