The Mpemba effect describes the situation in which a hot system cools faster than an identical copy at a colder temperature. Here, the authors present a theoretical model for the Mpemba effect through a second-order phase transition and showcase how this may describe the anti-ferromagnetic mean-field Ising model under the Glauber dynamics. The Mpemba effect describes the situation in which a hot system cools faster than an identical copy that is initiated at a colder temperature. In many of the experimental observations of the effect, e.g. in water and clathrate hydrates, it is defined by the phase transition timing. However, none of the theoretical investigations so far considered the timing of the phase transition, and most of the abstract models used to explore the Mpemba effect do not have a phase transition. We use the phenomenological Landau theory for phase transitions to identify the second order phase transition time, and demonstrate with a concrete example that a Mpemba effect can exist in such models.