Dynamic Frustration in PrAu$_2$(Si$_{1-x}$Ge$_x$)$_2$

We have recently proposed that frustration is dynamically induced in the spin glass, PrAu$_2$Si$_2$, a singlet ground state system, in which the interionic exchange is just sufficient to induce a magnetic moment. The degree of static disorder is far too small to produce spin glass freezing but dynamic fluctuations can destabilize the induced moments and frustrate the long-range magnetic correlations. We have studied the crystal field excitations in PrAu$_2$(Si$_{1-x}$Ge$_x$)$_2$, for which long-range order is stabilized at $x\approx12$\%. The excitation energy is independent of $x$ but inhomogeneous broadening increases linearly for $x<0.2$, \textit{i.e.}, long-range order is stabilized even though static disorder is increasing. Tuning the dynamic frustration with concentration or pressure could provide a test of the concept of ``avoided criticality'' in glassy systems.