Spin model for inverse melting and inverse glass transition

A spin model that displays inverse melting and inverse glass transition is presented and analyzed. Strong degeneracy of the interacting states of an individual spin leads to entropic preference of the ferromagnetic phase, while lower energy associated with the noninteracting states yields a paramagnetic phase as temperature decreases. An infinite range model is solved analytically for constant paramagnetic exchange interaction, while for its random exchange analogous results based on the replica symmetric solution are presented. The qualitative features of this model are shown to resemble a large class of inverse melting phenomena. First and second order transition regimes are identified.