Long-range order and low-energy spectrum of diluted 2D quantum AF
  The problem of diluted two-dimensional (2D) quantum antiferromagnet (AF) on a square lattice is studied using spin-wave theory. The influence of impurities on static and dynamic properties is investigated and a good agreement with experiments and Monte Carlo (MC) data is found. The hydrodynamic description of spin-waves breaks down at characteristic wavelengths $\Lambda\agt\exp(\frac{const}{x})$, $x$ being an impurity concentration, while the order parameter is free from anomalies. We argue that this dichotomy originates from strong scattering of the low-energy excitations in 2D. 
A. L. Chernyshev, Y. C. Chen, and A. H. Castro Neto (UC Riverside)