Elastic theory of flux lattices in presence of weak disorder

TL;DR

This paper develops an elastic theory for flux lattices in weakly disordered environments, identifying distinct regimes of behavior and providing quantitative predictions for experimental signatures.

Contribution

It introduces a combined Gaussian variational and renormalization group approach to analyze flux lattice displacements under weak disorder, clarifying crossovers and phase behavior.

Findings

Identifies three regimes: Larkin, Random Manifold, and quasi-ordered.

Predicts universal logarithmic growth of displacements in certain regimes.

Suggests existence of a Bragg glass phase with algebraic Bragg peaks in 3D.

Abstract

The effect of disorder on flux lattices at equilibrium is studied quantitatively in the absence of free dislocations using both the Gaussian variational method and the renormalization group. Our results for the mean square relative displacements clarify the nature of the crossovers with distance. We find three regimes: (i) a short distance regime (``Larkin regime'') where elasticity holds (ii) an intermediate regime (``Random Manifold'') where vortices are pinned independently (iii) a large distance, quasi-ordered regime where the periodicity of the lattice becomes important and there is universal logarithmic growth of displacements for $2<d<4$ and persistence of algebraic quasi-long range translational order. The functional renormalization group to $O(\epsilon=4-d)$ and the variational method, agree within $10\%$ on the value of the exponent. In $d=3$ we compute the crossover function between the three regimes. We discuss the observable signature of this crossover in decoration experiments and in neutron diffraction experiments on flux lattices. Qualitative arguments are given suggesting the existence for weak disorder in $d=3$ of a `` Bragg glass '' phase without free dislocations and with algebraically divergent Bragg peaks. In $d=1+1$ both the variational method and the Cardy-Ostlund renormalization group predict a glassy state below the same transition temperature $T=T_c$, but with different behaviors. Applications to $d=2+0$ systems and experiments on magnetic bubbles are discussed.