Improved analysis of the Landau-de Gennes model for the nematic state

A perturbation analysis of the Landau-de Gennes model for the nematic-isotropic phase transition is made. Particular attention is given to the calculation of the difference between the transition temperature $T_c$ and the temperature $T^{*}$. The temperature $T^{*}$ is the extrapolated divergence point for isotropic phase fluctuations. For space dimension greater than four, the calculation yields smaller values for this difference than does the mean-field approximation. Since smaller values are in the direction of better agreement with experiment the calculation supports the point of view that the Landau-de Gennes model is a correct phenomenological description of the nematic state.