Two-spin cluster theory for the Blume-Capel model with arbitrary spin

A two-spin cluster effective field theory for the Blume-Capel model with arbitrary spin S is presented by making use of exact spin identities and taking advantage of the differential operator technique. The dependence of the transition temperature is studied as a function of the single-ion anisotropy field strength for the particular cases S = 1, 3/2 and 2. The results are compared to those of the single-spin cluster theory recently reported in the literature as well as to other methods. In particular, it is shown that the present approach correctly distinguishes the geometry of the lattice structure beyond its coordination number.