Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

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Abstract
Recent attempts to generalize the classical Onsager theory of nematic ordering to finite-density systems of finite-length hard convex bodies are related and compared. It is pointed out that, although good results can be obtained in three dimensions (3D), in two dimensions (2D) the underlying factorization approximation of the radial and angular variables always implies a second-order isotropic-nematic transition instead of the crossover from a weakly first-order transition to a continuous (Kosterlitz-Thouless) transition as seen in the simulations. The quantitative agreement with the simulations is also much poorer in 2D than in 3D. On the contrary, for large spatial dimensions these theories become exact.