  An anisotropic t-J-U model Hamiltonian is used to model electron behaviour in
quasi-2d materials in the dilute limit, and as a highly simplified
representation of the weakly coupled CuO2 planes of the high-Tc cuprates we
model the very poor out-of-plane conductivity via the complete suppression of
interplanar hopping. However, we do include the very weak interplanar
superexchange, and are thus considering a model of exchange-coupled planes. For
an isotropic three-dimensional system in the dilute limit, we find that the
formation of two-particle bound states requires Jc/t ~ 5.9. Also, it is known
that Jc/t = 2 for a 2d square lattice. However, for our model of
exchange-coupled planes any infinitesimal interplanar exchange (Jc = 0) is
adequate to form bound states.
