The disordered ground state of quantum critical Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$*

We present neutron scattering data that show that magnetic ordering in the vicinity of a quantum critical point is restricted to short length scales. Remarkably, the spatial extent of the magnetic correlations is independent of the inter- moment distances. We argue that our data on Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$ demonstrate that quantum fluctuations disorder the system and dilute the magnetic moments to such an extent that the response of the system is disorder dominated. Our observations naturally explain how E/T- scaling is possible in systems whose apparent dimensionality is above the upper critical dimension.