We re-examine the Lebwohl-Lasher model of the isotropic-nematic liquid crystal phase transition as a function of dimensionality d, using the Bethe-Peierls approximation. Our results suggest that the transition temperature approaches the mean-field limit asymptotically as d -1, not, as suggested by recent computer simulations, as d -1·5.
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Michael Allen (1989) studied this question.
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