The first order phase transitions in the multisite spin-1/2 model on a pure Husimi lattice

We investigate the multisite spin-1/2 Ising-like model in the presence of the external magnetic field on the pure Husimi lattice with three sites in the elementary polygon (p=3) and coordination number z=6 which represents the simplest approximation of the model on the two-dimensional triangular lattice which takes into account its elementary geometric structure. It is shown that, depending on the values of the parameters of the model, at maximum three different phases exist in the model. The existence of the first order phase transitions between various phases is demonstrated and studied in detail. The total magnetization per site is analyzed as function of the temperature as well as of the external magnetic field. It is shown that for low temperatures the model exhibits a typical behavior of geometrically frustrated systems. All possible ground states of the model are found and discussed.