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Using the dynamical mean-field theory (DMFT) we study the paramagnetic phaseof the Hubbard model with the density of states (DOS) corresponding to thethree-dimensional cubic lattice and the two-dimensional square lattice, as wellas a DOS with inverse square root singularity. We show that the electroncorrelations rapidly smooth out the square-root van Hove singularities (kinks)in the spectral function for the 3D lattice and that the Mott metal-insulatortransition (MIT) as well as the magnetic-field-induced MIT differ only littlefrom the well-known results for the Bethe lattice. The consequences of thelogarithmic singularity in the DOS for the 2D lattice are more dramatic. Athalf filling, the divergence pinned at the Fermi level is not washed out, onlyits integrated weight decreases as the interaction is increased. While the Motttransition is still of the usual kind, the magnetic-field-induced MIT fallsinto a different universality class as there is no field-induced localizationof quasiparticles. In the case of a power-law singularity in the DOS at theFermi level, the power-law singularity persists in the presence of interaction,albeit with a different exponent, and the effective impurity model in the DMFTturns out to be a pseudo-gap Anderson impurity model with a hybridizationfunction which vanishes at the Fermi level. The system is then a generalizedFermi liquid. At finite doping, regular Fermi liquid behavior is recovered.

Van Hove singularities in the paramagnetic phase of the Hubbard model: a DMFT study