  The heavy fermion system CeCu$_{6-x}$Ag$_x$ is studied at its
antiferromagnetic quantum critical point, $x_c=0.2$, by low temperature ($T\geq
50$ mK) specific heat, $C(T)$, and volume thermal expansion, $\beta(T)$,
measurements. Whereas $C/T\propto \log(T_0/T)$ would be compatible with the
predictions of the itinerant spin-density-wave (SDW) theory for two-dimensional
critical spin fluctuations, $\beta(T)/T$ and the Gr\"uneisen ratio,
$\Gamma(T)\propto \beta/C$, diverge much weaker than expected, in strong
contrast to this model. Both $C$ and $\beta$, plotted as a function of the
reduced temperature $t=T/T_0$ with $T_0=4.6$ K are similar to what was observed
for YbRh$_2$(Si$_{0.95}$Ge$_{0.05}$)$_2$ ($T_0=23.3$ K) indicating a striking
discrepancy to the SDW prediction in both systems.
