  We study a mean-field spin model with three- and two-body interactions. The
equilibrium measure for large volumes is shown to have three pure states, the
phases of the model. They include the two with opposite magnetization and an
unpolarized one with zero magnetization, merging at the critical point. We
prove that the central limit theorem holds for a suitably rescaled
magnetization, while its violation with the typical quartic behavior appears at
the critical point.
