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We propose an approach to a multiscale problem in the theory of thermotropicuniaxial nematics based on the method of statistical field theory. Thisapproach 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 transitionto the parameters of a molecular model of uniaxial nematics, which we take tobe a lattice gas model of nematogenic molecules interacting via a short-rangedpotential. We obtain general constraints on the temperature and volume fractionof nematogens for the Landau-de Gennes theory to be stable against molecularorientation fluctuations at quartic order. In particular, for the case of afully occupied lattice, we compute the values of the isotropic-nematictransition temperature and the order parameter discontinuity predicted by (i) acontinuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) aLebwohl-Lasher-type model with a nematogenic interaction of finite range. Wefind that the predictions of (i) are in reasonably good agreement with knownresults of MC simulation.

A multiscale approach to liquid crystal nematics via statistical field theory