Branching of symmetric solution of molecular field equation

Branching of a completely symmetric solution of the molecular field equation is investigated under the assumption fnat the configuration space of a molecule is a certain group $Q$. The scheme can be used to describe orientationally ordered and spacemodulated structures. Phase transitions from an isotropic liquid to the nematic, cholesteric, and conic phases are considered. The relationship between the phase-transition characteristics (order, Curie point, symmetry of the newly formed phase) and the potential of the intermolecular interaction is established. Investigation of the isolated isotropic-liquid–two-axis-nematic phase transition point has shown that this is not always a second-order transition. The possible existence of a one-dimensional modulated structure having smectic-$A$ symmetry is predicted. The corresponding phase transition follows a scenario different from that of the isotropie-liquid–smectic-$A$ phase transition.