New mean-field theory applied to antiferromagnetic spin models with geometric frustration

In this work, we presented a new theoretical approach based on Mean-Field Theory, employing a hybrid Hamiltonian (spin/charge) in the spin-1/2 antiferromagnetic Ising model on lattices exhibiting geometric frustration. The study was conducted using the mean-field theory derived from Bogoliubov’s inequality to obtain a generic expression for the free energy in any frustrated lattice. To validate this theoretical approach, we applied the model to both the pyrochlore and kagome lattices occupied by spin-1/2 described by antiferromagnetic Ising model. The results revealed key features of geometric frustration in the studied structures, consistent with previous results reported in the literature, such as residual entropy, the characteristic behavior of the specific heat, and the emergence of plateaus in the magnetization curves.