Influence of multisite interaction on thermodynamics and ground-state degeneracies of frustrated magnetic systems with pyrochlore structure: An exact theoretical analysis

The antiferromagnetic spin-1∕2 Ising model with the multisite interaction in the presence of the external magnetic field is investigated on the tetrahedron recursive lattice, which represents a suitable and effective approximation of frustrated magnetic materials with pyrochlore structure. It is shown that the model belongs to the rather restricted set of exactly solvable models and exhibits unique solution for all values of the model parameters. The exact expression for the free energy per site is found and the magnetization and entropy properties of the model are investigated in detail. The system of all ground states of the model under the influence of the multisite interaction is identified and their magnetization properties and the values of all residual entropies are found exactly. It is shown that not only the strength but also the sign of the multisite interaction has the significant impact on the properties of the model and that, depending on the value of the multisite interaction in comparison to the absolute value of the antiferromagnetic nearest-neighbor interaction, the model exhibits the existence of three ground states of different orders with the same value of the magnetization equal to zero but with the residual entropies which are considerably different, i.e., with different macroscopic degeneracies.