Stability analysis of a two-dimensional uniaxial vortex glass.

Abstract

The simplest model of a vortex glass is considered which is applicable for the description of a twodimensional 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. I. INTRODUCTION The discovery of the high-Tc superconconducting materials have essentially increased the possibilities for the experimental observations of various phenomena related with the presence of vortices in superconductors ~vortex lattice melting, pinning, creep and so on!. This has led to the active development of theoretical investigation of these phenomena and the appearance of many new ideas ~for a recent review see Ref. 1!. In particular a suggestion has been made that at low temperatures a phase should exist in which the motion of the vortices is quenched by disorder and therefore the linear resistance is absent. 2,3 The properties of this phase ~including the multitude of metastable states separated by the diverging barriers! are expected to be more or less analogous to those of widely discussed infinite-range spin-glass models 4 and therefore it is usually called a vortex glass. It has been suggested 2,5 that the simplest model which allows one to analyze the large scale properties of a vortex crystal ~or charge-density wave! interacting with a random potential can be described by the Hamiltonian