We present specific heat measurements of 4% Rh-doped U(Ru,Rh)2Si2 at magnetic fields above the proposed metamagnetic transition field Hm~34 T, revealing striking similarities to the isotructural Ce analog CeRu2Si2, suggesting that strongly renormalized hybridized band models apply equally well to both systems. The vanishing bandwidths as H --> Hm are consistent with a putative quantum critical point close to Hm. The existence of a phase transition into an ordered phase in the vicinity of Hm for 4% Rh-doped U(Ru,Rh)2Si2, but not for CeRu2Si2, is consistent with a stronger super-exchange in the case of the U 5-f system, with irreversible processes at the transition revealing a strong coupling of the 5f orbitals to the lattice, most suggestive of orbital or electric quadrupolar order.
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