A note on the Ising models with four-spin interactions

The phase diagrams of the Ising models with two types of four-spin interactions on honeycomb lattice, which acts only between the nearest-neighbor sites or to the nearest- and next-nearest-neighbor sites in addition to the conventional pair interactions, are investigated within the two frameworks of the Zernike approximation and the correlated effective-field approximation, using the differential operator technique. The results indicate that the Ising model with a nearest-neighbor four-spin interaction should be treated as an interesting physical system, being different from the system with nearest- and next-nearest-neighbor four-spin interactions.