The Blume-Capel model for spins S=1 and 3∕2 in dimensions d=2 and 3

Expansions through the 24th order at high-temperature and up to 11th order at low-temperature are derived for the main observables of the Blume-Capel model on bipartite lattices (sq,sc and bcc) in 2d and 3d with various values of the spin and in presence of a magnetic field. All expansion coefficients are computed exactly as functions of the crystal and magnetic fields. Several critical properties of the model are analyzed in the two most studied cases of spin S=1 and S=3∕2.