Tetracritical and novel tricritical points in a model magnet

A generalized three-dimensional spherical model of magnetism is shown to exhibit a rich variety of phase equilibria and critical phenomena, including critical points not found in any classical Landau theory, but observed recently in a model of equilibrium polymerization. The model exhibits a tetracritical point at which four phases, two nonmagnetic and two magnetically ordered, become identical, as well as novel tricritical points at which the magnetic and wing critical lines meet at a cusp. The model also exhibits additional transitions, not found in the polymerization model