Random-exchange quantum Heisenberg antiferromagnets on the square   lattice
  The ground state properties of random-exchange spin-1/2 Heisenberg antiferromagnets on the square lattice are investigated using a combination of quantum Monte Carlo simulations, exact numerical diagonalizations, and spin wave calculations. Whereas arbirarily weak disorder has a drastic effect on 1d Heisenberg AFM, we find that in two dimensions the characteristics of the ground state like long-range order is robust even against strong disorder. While the antiferromagnetic order parameter and the spin stiffness are exponentially reduced for singular exchange distributions, they vanish only in the limit of infinite randomness. 
Nicolas Laflorencie, Stefan Wessel, Andreas Laeuchli, Heiko Rieger