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 …