  We propose an approach to a multiscale problem in the theory of thermotropic
uniaxial nematics based on the method of statistical field theory. This
approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$
of the Landau-de Gennes free energy for the isotropic-nematic phase transition
to the parameters of a molecular model of uniaxial nematics, which we take to
be a lattice gas model of nematogenic molecules interacting via a short-ranged
potential. We obtain general constraints on the temperature and volume fraction
of nematogens for the Landau-de Gennes theory to be stable against molecular
orientation fluctuations at quartic order. In particular, for the case of a
fully occupied lattice, we compute the values of the isotropic-nematic
transition temperature and the order parameter discontinuity predicted by (i) a
continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a
Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We
find that the predictions of (i) are in reasonably good agreement with known
results of MC simulation.
