Quantum destruction of stiffness in diluted antiferromagnets and superconductors

The reduction of 2D superconducting or antiferromagnetic order by random dilution is studied as a model for the 2D diluted Heisenberg antiferromagnet (DHAF) La$_2$Cu$_{1-p}$(Zn,Mg)$_p$O$_4$ and randomly inhomogeneous 2D suerconductors. We show in simplified models that long-range order can persist at the percolation threshold despite the presence of disordered one-dimensional segments, contrary to the classical case. When long-range order persists to the percolation threshold, charging effects (in the superconductor) or frustrating interactions (in the antiferromagnet) can dramatically modify the stiffness of the order. This quantum destruction of stiffness is used to model neutron scattering data on La$_2$Cu$_{1-p}$(Zn,Mg)$_p$O$_4$. In a certain simplified model, there is a sharp stiffness transition between ``stiff'' and ``floppy'' ordered phases.