Disordered XY model: effective medium theory and beyond

Abstract

We study the effect of uncorrelated random disorder on the temperature dependence of the superfluid stiffness in the two-dimensional classical XY model. By means of a perturbative expansion in the disorder potential, equivalent to the T-matrix approximation, we provide an extension of the effective-medium-theory result able to describe the low-temperature stiffness, and its separate diamagnetic and paramagnetic contributions. These analytical results provide an excellent description of the Monte Carlo simulations for two prototype examples of uncorrelated disorder. Our findings offer an interesting perspective on the effects of quenched disorder on longitudinal phase fluctuations in two-dimensional superfluid systems.

arXiv comment11 pages, 5 figures

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• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Destruction of superconductivity through phase fluctuations in ultrathin a-MoGe films
• Experimental realization of a 3D long-range random hopping model
• An optical Ising spin glass simulator with tuneable short range couplings
• Thermodynamic phase diagram of the competition between superconductivity and charge order in cuprates
• Inhomogeneous phase stiffness in two-dimensional $s$-wave disordered superconductors
• Superfluid response of two-dimensional filamentary superconductors
• Uniformly frustrated XY model: strengthening of the vortex lattice by intrinsic disorder