New effective field theory in a cluster with n-sites correlating with n-free spins: Ferrimagnetic and Antiferromagnetic

The Ising model is a central tool in the study of spin systems, with various generalizations to describe complex magnetic orderings. This work proposes a new application of the effective field theory (EFT) using clusters with $n$-sites, extending previous approaches to ferrimagnetic and antiferromagnetic states. Two specific cases are analyzed: a three-layer system of triangular lattices for ferrimagnetism and a square lattice for antiferromagnetism. The results include magnetizations, magnetic susceptibilities, and phase diagrams, showing that increasing the number of sites in the cluster improves accuracy, bringing the values closer to those obtained from Monte Carlo simulations. The proposed approach offers an efficient tool to study magnetic systems with different couplings and structural configurations. Although the new method presents improvements in numerical results, it is important to emphasize that its main contribution lies in introducing a more efficient approach, with simplifications in mathematical expansions aimed at reducing the computational time required in studies of this nature.