Quantum critical points (QCPs) are widely accepted as a source of a diverse set of collective quantum phases of matter. A central question is how the order parameters of phases near a QCP interact and determine the fundamental character of the critical dynamics which drive the quantum critical behavior. One of the most interesting proposals for the quantum critical behavior that occurs in correlated electron systems is that the behavior may arise from local, as opposed to long wavelength, critical fluctuations of the order parameter. The local criticality is believed to give rise to energy over temperature ($E/T$) scaling of the dynamic susceptibility with a fractional exponent near the quantum critical point (QCP). Here we show that $E/T$ scaling is indeed observed for CeCu$_{6-x}$Ag$_x$ but on closer inspection, the fluctuations can be separated into two components, implying that multiple order parameters play an important role in the unconventional critical behavior. Additionally, when the fluctuations corresponding to the magnetically ordered side of the phase diagram are separated, they are found to be three dimensional and to obey the scaling behavior expected for long wavelength fluctuations near an itinerant antiferromagnetic QCP.
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