Tricritical behaviour of the ferromagnetic Blume-Capel model with first- and second-neighbour interactions

A ferromagnetic Blume-Capel model with first- and second-neighbour interactions is investigated by the use of the effective-field theory with correlations. The general expressions for evaluating the second-order phase transition and the tricritical point are obtained. Particular emphasis is given to the square lattice for which the dependence of the position of the tricritical point on the relative strengths of the second- and first-neighbour interactions is investigated.