Effectiveness of the recursive-lattice technique in the investigation of magnetic systems with the pyrochlore structure.

A well-defined higher recursive approximation of the pyrochlore lattice is introduced and its relevance and effectiveness for the systematic investigation of magnetic systems with the pyrochlore structure is studied within the classical antiferromagnetic as well as ferromagnetic spin-1/2 Ising model in the presence of the external magnetic field. The exact solution of the model is found with the explicit analytic expression for the free energy per site of the lattice. The magnetization and entropy properties of all ground states of the antiferromagnetic model are determined and compared to those obtained within the lower recursive approximation of the model on the recursive tetrahedral lattice. The exact analysis of the residual entropies of the model on the introduced recursive lattice explicitly shows that the well-known Pauling entropy of the water ice cannot represent the true residual entropy of the antiferromagnetic model on the regular pyrochlore lattice in the zero external magnetic field. The improvement of the value of the critical temperature of the ferromagnetic model obtained within the introduced higher recursive approximation is also discussed. The analysis performed demonstrates the great efficiency of recursive approximations in the investigation of various magnetic systems with the pyrochlore structure, especially for frustrated antiferromagnetic systems.