Series expansions are used to treat the randomly diluted spin-1/2 Heisenberg antiferromagnet at zero temperature. A series is obtained at zero temperature in powers of the concentration for many correlation functions and for the correlation length from which static, dynamic, and crossover exponents are estimated. The correlation length exponent is found to be 0.77±0.10 in two dimensions. The critical concentration for the appearance of long-range order is indistinguishable from the percolation threshold.
We study the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets with both Ising anisotropy and spatial anisotropy. We represent the spin operators in terms of spin-density operators and spin-phase operators. Then for spin-1/2 antiferromagnets, within a simple harmonic approximation, we obtain expressions for the spin correlations in the ground state. For the one-dimensional linear chain, we find that the two leading terms in spin correlation are (-1
)rc/${\mathit{r}}^{\mathrm{\ensuremath{\eta}}}$-
c1/
r2 for large distance r. The power \ensuremath{\eta} depends on the Ising anisotropy, and \ensuremath{\eta}=0.405 at XY point and \ensuremath{\eta}=1.062 at Heisenberg point. For the two-dimensional square lattice, there is long-range staggered magnetization, and the dependence of magnetization on Ising anisotropy is given. For the crossover from one-dimensional linear chain to two-dimensional square lattice, we find that the disorder-order transition occurs as long as the interchain coupling is introduced. We believe that our method gives a unified approach to the long-range behavior of spin correlations in low-dimensional spin-1/2 antiferromagnets.