The Exact Solution of the Anti-ferromagnetic Ising Model with Multisite Interaction on the Simplest Pure Husimi Lattice

Abstract

We investigate the anti-ferromagnetic spin- $$1/2$$ Ising model with the presence of the multisite interaction on the pure Husimi lattice with three sites in the elementary polygon ( $$p=3$$ ) and coordination number $$z=4$$ . It represents the simplest approximation of the corresponding anti-ferromagnetic Ising model on the two-dimensional Kagome lattice which takes into account effects of frustration. The exact analytical solution of the model is found and discussed. It is shown that, regardless of the strength of the multisite interaction, the model does not exhibit any kind of the phase transitions. The behavior and properties of the magnetization as the function of the parameter which controls the strength of the multisite interaction and as the function of the external magnetic field are studied in detail. The existence of the magnetization plateaus for low temperatures is shown. In addition, all possible ground states of the model are found and their properties are discussed.