Frustration and Phase Transitions in Ising Model on Decorated Square Lattice

The Ising model on a square lattice with arbitrary number of decorating spins, considering both the interactions between nodal and decorating spins is examined. A plethora of peculiarities such as heat capacity splitting, generation and suppression of multiple phase transitions and several kinds of partial ordering are thoroughly scrutinized. A rigorous analytical expression for the partition function closely resembling the one obtained by Onsager is presented.