Four particle cluster approximation for the Maier–Saupe model of the isotropic–nematic phase transition

The cluster variation theory for the Maier–Saupe model of the isotropic–nematic phase transition is extended to the four-particle level. As in the case of the Heisenberg ferromagnet, the irregularities of the three-particle cluster approximation applied to cubic lattices, where there are no triangles of nearest neighbors, disappear. The extension from three- to four-particle clusters yields improved values of all quantities, characteristic for the phase transition.