Kagome antiferromagnet with the multisite interaction in the external magnetic field: Exact results within higher recursive-lattice approximation

The so-called 3-star kagome-like recursive-lattice approximation is introduced that significantly more accurately approximates the basic geometric structure of the real two-dimensional kagome lattice. The exact solution of the antiferromagnetic Ising model in the external magnetic field and with the presence of the three-site interaction within each elementary triangle of the introduced recursive lattice is found. The free energy of the model is derived and the system of all ground states is determined. The exact expressions for the residual entropies and magnetization values of all ground states of the model are derived. The magnetic and thermodynamic properties of the model are discussed in detail and are compared to those obtained in the framework of the lower recursive-lattice approximations of the model as well as to the existing exact results on the real kagome lattice. The performed analysis, on the one hand, confirms the validity of two early stated hypotheses about the behavior of residual entropies and magnetization properties of all ground states of frustrated magnetic systems on the recursive lattices and, on the other hand, allows one to make also nontrivial conclusions about the fundamental properties of the model on the real kagome lattice although the corresponding exact solutions are still not available. Last but not least, the performed analysis once again confirms the effectiveness of the recursive-lattice technique for the analysis of frustrated magnetic systems.