First order phase transitions in the antiferromagnetic Ising model on a pure Husimi lattice

The antiferromagnetic spin-1/2 Ising model on the pure Husimi lattice with three sites in the elementary polygon (p=3$p=3$) and the coordination number z=6$z=6$ is investigated which represents the simplest approximation of the antiferromagnetic Ising model on the regular triangular lattice which takes into account effects of geometric frustration. The region of parameters is found in which two physical phases coexist. In addition, the existence of the first order phase transitions between these two coexisting phases is demonstrated and investigated in detail. A detailed analysis of the magnetization properties of the model is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed.