Long-range order and low-energy spectrum of diluted 2D quantum antiferromagnet

The problem of a diluted two-dimensional quantum antiferromagnet 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 data is found. The hydrodynamic description of spin waves breaks down at characteristic wavelengths Lambda greater than or similar to exp(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 two dimensions.