Quantum critical 5f electrons avoid singularities in U(Ru,Rh)(2)Si-2

We present specific heat measurements of 4% Rh-doped URu2Si2 at magnetic fields around the proposed metamagnetic transition field H(m)similar to 34 T, revealing striking similarities to the isotructural Ce analog CeRu2Si2 for H > H-m. This suggests that strongly renormalized hybridized-band models apply equally well to both systems. The vanishing bandwidths as H -> H-m are consistent with a quantum-critical point close to H-m. The existence of a phase transition into an ordered phase in the vicinity of H-m for 4% Rh-doped URu2Si2, but not for CeRu2Si2, is consistent with a stronger superexchange in the case of the U 5f system. Irreversible processes at the transition indicate a strong coupling of the 5f orbitals to the lattice, most suggestive of electric quadrupolar order.