The model studied in this dissertation consists of planes, in which the nodal spins (vertices of a square lattice) have antiferromagnetic (J1 and J2) interactions with the first (J1 < 0) and second (J2 < 0) neighboring spins (representing the interactions in the bond between the Cu −Cu copper ions in the CuO2 plane) and with ferromagnetic interaction (JF > 0) with the decorator spins (simulating the Cu − O interactions) randomly distributed quenched (quenched) over a two-dimensional lattice, and finally , the nodal spins between planes have weak antiferromagnetic interaction (λ J1 < 0, λ = 10−5). In this model, the action of a magnetic field and the effective interaction Je f between the nodal spins are considered, determined with the contribution of the decorator spin, through the decoration-iteration transformation technique. The phase transition of the model was studied through the effective field theory for a cluster with a spin, combined with the differential operator technique. Then, we discussed the critical concentration pc at which the Ne'el temperature tends to zero for various values of the spin frustration parameters α1 and α2 (α1 = JF /J1, α2 = J2/J1) under the influence of the magnetic field H. For some of these values, we observe a reentrant behavior at low temperatures. Phase diagrams were also obtained in the plane ( KB TN, H ), and for some values of H , in the planes ( p, KB TN ), (KB TNKB TNJ1 J1KB TNJ1, α1), (J1 , α2) and ( λ ,J1 ). Finally, the dependence of the sublattice magnetization as a function of temperature was calculated, helping to determine the uniform (m) and remaining (residual, ms) magnetizations, in order to analyze the existence of the spin frustration phenomenon, and the reentrant behavior in the phase diagrams of the planes ( KB TN , m ) and ( KB TN , ms) under the effect of the magnetic field.
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