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

Abstract

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.