We study Onsager's free energy functional for nematic liquid crystals with an orientation parameter on a unit circle. For a class of interaction potentials we obtain explicit expressions for all critical points, analyze their stability, and construct the corresponding bifurcation diagram. We also derive asymptotic expansions of the equilibrium density of orientations near the critical and zero temperatures.
"A Note on the Onsager Model of Nematic Phase Transitions." Commun. Math. Sci. 3 (1) 21 - 26, March 2005.