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 ${\mathrm{La}}_{2}{\mathrm{Cu}}_{1\ensuremath{-}x}{M}_{x}{\mathrm{O}}_{4} (M=\mathrm{Zn},\mathrm{Mg}).$ We calculate the staggered magnetization at zero temperature, ${M}_{s}(x),$ the magnetic correlation length, $\ensuremath{\xi}(x,T),$ the NMR relaxation rate, ${1/T}_{1}(x,T),$ and the N\'eel temperature, ${T}_{N}(x),$ in the renormalized classical regime. Due to quantum fluctuations we find a quantum critical point at ${x}_{c}\ensuremath{\approx}0.305$ at lower doping than the two-dimensional percolation threshold ${x}_{p}\ensuremath{\approx}0.41.$ We compare our results with the available experimental data.