Abstract
From the application of the theory of the self-consistent mean field (Maier-Saupe theory) it is shown that in two-dimensional systems with a continuous distribution of the orientations of the elements passage from the isotropic to the ordered state occurs as a phase transition of the second kind (as distinct from three-dimensional systems where the corresponding transition is a phase transition of the first kind). Because of fluctuational instability of far order in a continual two-dimensional system the results of the meann field theory may be applied only to portions of finite size. In two-dimensional systems with discrete orientations of the elements (lattice models) transitions to the ordered state may be both of the first and second kinds depending on the symmetry of the lattice.
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