Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume-Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature.The obtained results improve over effective field type results.Comment: 13 page

Tri-critical behavior of the Blume Capel model on a diamond lattice

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq: 147716/2014.4The mean field approximation results are obtained in a five-site cluster on the diamond lattice from the Bogoliubov inequality. Spin correlation identities for the Blume-Capel model on diamond lattice are derived from a five-site cluster and used to obtain an effective field approximation. The free-energy, magnetization, critical frontiers and tricritical points are obtained from the mean field approximation and the effective field approximation and are compared to those obtained by other methods. From the mean-field approximation, we also studied the unstable and metastable states besides the stable states present in the model