Stability analysis of a two-dimensional uniaxial vortex glass

The simplest model of a vortex glass is considered which is applicable for the description of a two-dimensional uniaxial vortex crystal formed by the fluxon lines in a large area Josephson junction with inhomogeneous width. The analysis is performed in replica representation in terms of a free-energy functional which depends on the renormalized correlation function. The properties of different solutions of the Dyson equation are considered, the main attention being devoted to investigating the stability of these solutions. In particular the solution with the one-step replica symmetry breaking which corresponds to the absolute maximum of free energy is shown to be always stable (when it exists at all). The unimportance of higher-order corrections for the form of the asymptotic behavior of the correlation function in the phase with the one-step replica symmetry breaking is also demonstrated.