  We investigate the connections between some simple Maier-Saupe lattice
models, with a discrete choice of orientations of the microscopic directors,
and a recent proposal of a two-tensor formalism to describe the phase diagrams
of nematic liquid-crystalline systems. This two-tensor proposal is used to
formulate the statistical problem in terms of fully-connected lattice
Hamiltonians, with the local nematic directors restricted to the Cartesian
axes. Depending on the choice of interaction parameters, we regain all of the
main features of the original mean-field two-tensor calculations. With a
standard choice of parameters, we obtain the well-known sequence of isotropic,
uniaxial, and biaxial nematic structures, with a Landau multicritical point.
With another suitably chosen set of parameters, we obtain two tricritical
points, according to some recent predictions of the two-tensor calculations.
The simple statistical lattice models are quite easy to work with, for all
values of parameters, and the present calculations can be carried out beyond
the mean-field level.
