An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model

•We developed spin models to study real magnetic systems.•We study the thermodynamic and magnetic properties of the ferromagnetism.•We enhanced a mean-field theory applied in spins models.

We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value kBTc/J≃2.27905±0.00141kBTc/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained.