Resumen de Symmetry Adapted Molecular-Field Theory for Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion at Low Temperature
We have analyzed some properties of mean field theories of thermotropic biaxial liquid crystals with ($D_{2h}$) symmetry. The study consists of two parts. In the first part we reexamine the standard theory due to Virga and coworkers. We introduce a convenient symmetry-adapted parameterization which allows the phase diagram to be displayed in an explicitly symmetry-preserving triangle. In the second part we use the Laplace approximation to examine the low temperature properties of the liquid crystal order parameters. Two of these (conventionally, $D,P$) are identically zero at zero temperature in a biaxially ordered phase and nonzero at low temperatures in the liquid crystalline phases but are again zero at higher temperatures in the isotropic phase. We use a low temperature expansion to derive an expression for the dominant terms in the free energy. This functional is minimized to obtain the low temperature properties of the order parameters $D,P$
