  The mean field approximation results in the mixed spin 1/2 Ising model and
spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from
the Bogoliubov inequality. The Gibbs free energy, magnetization and critical
frontiers are obtained. Besides the stable branches of the order parameters, we
obtain the metastable and unstable parts of these curves and also find phase
transitions of the metastable branches of the order parameters. The
classification of the stable, metastable and unstable states is made by
comparing the free energy values of these states.
