Here, we unveil evidence for a quantum phase-transition in CeCu_2Ge_2 which displays both an incommensurate spin-density wave (SDW) ground-state, and a strong renormalization of the quasiparticle effective masses (mu) due to the Kondo-effect. For all angles theta between an external magnetic field (H) and the crystallographic c-axis, the application of H leads to the suppression of the SDW-state through a 2^nd-order phase-transition at a theta-dependent critical-field H_p(theta) leading to the observation of small Fermi surfaces (FSs) in the paramagnetic (PM) state. For H || c-axis, these FSs are characterized by light mus pointing also to the suppression of the Kondo-effect at H_p with surprisingly, no experimental evidence for quantum-criticality (QC). But as $H$ is rotated towards the a-axis, these mus increase considerably becoming undetectable for theta > 56^0 between H and the c-axis. Around H_p^a~ 30 T the resistivity becomes proportional T which, coupled to the divergence of mu, indicates the existence of a field-induced QC-point at H_p^a(T=0 K). This observation, suggesting FS hot-spots associated with the SDW nesting-vector, is at odds with current QC scenarios for which the continuous suppression of all relevant energy scales at H_p(theta,T) should lead to a line of quantum-critical points in the H-theta plane. Finally, we show that the complexity of its magnetic phase-diagram(s) makes CeCu_2Ge_2 an ideal system to explore field-induced quantum tricritical and QC end-points.
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