Effective field theory for layered quantum antiferromagnets with nonmagnetic impurities

We propose an effective two-dimensional quantum nonlinear sigma model combined with classical percolation theory to study the magnetic properties of site diluted layered quantum antiferromagnets such as La₂Cu_1-xMₓO₄ (M=Zn,Mg). We calculate the staggered magnetization at zero temperature, Mₛ(x), the magnetic correlation length, ξ(x,T), the NMR relaxation rate, 1/T₁(x,T), and the N\'eel temperature, TN(x), in the renormalized classical regime. Due to quantum fluctuations we find a quantum critical point at xc≈0.305 at lower doping than the two-dimensional percolation threshold xₚ≈0.41. We compare our results with the available experimental data.