The model potentials Uij = -fL(rij)PL(cosβij) with rank L = 2, 4, 6, 8 have been studied using mean field theory. All the potentials yield a first order orientational phase transition with an entropy change increasing with the rank. The order parameters βJ do not always decrease regularly with increasing J as for the rank L = 2, Maier-Saupe, case.
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Claudio Zannoni (1979) studied this question.
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