Conductivity in a two-dimensional disordered model with anisotropic long-range hopping

We consider a two-dimensional system of particles localized on randomly distributed sites of a square lattice with anisotropic transition matrix elements between localized sites. The diagram and replica methods are used. The conductivity of a system in different limits of local sites and particles densities is calculated. The model is relevant to the problem of strong nonmagnetic impurities in superconductors with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$d_{x^2 - y^2 } $$ \end{document} symmetry of the order parameter.