2001/10/31 by Anders W. Sandvik · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.66.024418
published as Phys. Rev. B 66, 024418 (2002) · 18 pages, 21 figures (spin stiffness results added in v2)
arxiv created 2002/06/26 · openalex publication_date 2002/07/11 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The two-dimensional antiferromagnetic S=1/2 Heisenberg model with random site dilution is studied using quantum Monte Carlo simulations. Ground-state properties of the largest connected cluster on L\ifmmode×\else\texttimes\fiL lattices, with L up to 64, are calculated at the classical percolation threshold. In addition, clusters with a fixed number Nc of spins on an infinite lattice at the percolation density are studied for Nc up to 1024. The disorder averaged sublattice magnetization per spin extrapolates to the same nonzero infinite-size value for both types of clusters. Hence, the percolating clusters, which are fractal with dimensionality d=91/48, have antiferromagnetic long-range order. This implies that the order-disorder transition driven by site dilution occurs exactly at the percolation threshold and that the exponents are classical. The same conclusion is reached for the bond-diluted system. The full sublattice magnetization versus site dilution curve is obtained in terms of a decomposition into a classical geometrical factor and a factor containing all the effects of quantum fluctuations. The spin stiffness is shown to obey the same scaling as the conductivity of a random resistor network.