The spin-correlation length is used to set up a RG analysis of the Hubbard model (within RPA). We demonstrate that an identical critical behaviour is obtained by performing the macroscopic renormalization group analysis with the antisymmetric Landau interaction parameter. The beta functions for the half-filled and quarter-filled band cases have been evaluated.

Static, non-magnetic impurities give rise to gap states in a doped Mott-Hubbard antiferromagnetic insulator. The spectral and spatial features of these gap states are discussed, and it is argued that these gap states are responsible for the observed local-moment behaviour in zinc-doped cuprates.

The three-band Hubbard model — both pure and with static non-magnetic impurities — has been studied within a self-consistent numerical Hartree-Fock (HF) scheme. The system shows nesting properties only in the absence of direct O-O hopping. Spin excitations in the system are gapless with the existence of a Goldstone mode in the broken-symmetry state. The variation of spinwave velocity with Cu-site Coulomb repulsion shows a (1/(2U_d)+(1/Δ)) dependence in the strong-coupling limit. Each non-magnetic impurity in the system gives rise to two gap states for a particular spin and the local moment produced is robust even at finite concentration of mobile hole doping. The gapless Goldstone mode is preserved even in case of unequal concentration of impurities on the two sublattices.

The recent neutron scattering data for spin-wave dispersion in HoMnO₃ are well-described by an anisotropic Hubbard model on a triangular lattice with a planar (XY) spin anisotropy. Best fit indicates that magnetic excitations in HoMnO₃ correspond to the strong-coupling limit $U/t > \sim 15$, with planar exchange energy $J = 4t^{2}/U \simeq 2.5$ meV and planar anisotropy $\Delta U \simeq 0.35 $meV.