The different approximations that have been used in applying Bethe’s cluster model to the nematic-isotropic phase transition are examined. It is shown that the introduction of a higher order term in the mean field potential of an outer molecule of the cluster improves the consistency of the theory considerably. In particular, the importance of satisfying Chang’s relation is emphasized. Calculations are presented of the long and short range order parameters, heat of transition and specific heat for different values ofz, the number of nearest neighbours around any given molecule, for both nonpolar and antiparallel near neighbour correlations. Even the new mean field potential appears to be inadequate forz=3.

We have applied the Krieger-James approximation to a description of short range order effects in both ferro- and antiferromagnetism. In this method, a mechanical consistency condition is imposed on the probability distribution of a pair of near neighbours in a cluster of (Z+1) ions. The resulting theory is analytically equivalent to the familiar constant coupling approximation, thus ensuring thermodynamic equilibrium of the system.