THE PHASE-DIAGRAM OF THE 2D ISING-MODEL WITH ANISOTROPIC NEXT-NEAREST-NEIGHBOR AND 4-SPIN INTERACTIONS

In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions ha s been studied. The ground states and energy of the model have been ob tained. The model is equivalent to an eight-vertex model on its dual l attice. In some special cases, the model can be solved exactly as a ze ro-field eight-vertex model or a free-fermion model. Explicit phase di agrams are obtained exactly.