Modelos magnéticos com frustração e diluição
Pacobahyba, Josefa Teixeira de Mendonça
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In this work, we investigate the effect of dilution and frustration in the thermodynamic properties and the phase diagrams using the quasi-two-dimensional Heisenberg and Ising models. We use the Zubarev Green´s function formalism and obtain the magnetic properties of the quasi-two-dimensional antiferromagnetic spin ½ Heisenberg model. We determine the limit of the stability of the antiferromagnetic phase as a function of the concentration of the holes in the CuO2 plane and dilution of the Cu by Zn. We simulate the point of maximum of the phase diagram in the plane (T,z) following the experimental data for the La2-xSrxCu1-zZnzO4 compounds. In the Heisenberg model the effect of the frustration is simulated by the parameter λ=λ0(1-x/xc), which measures the interaction between the CuO2 planes. The effect of dilution present in the xy-plane is described theoretically by a small value for z through an effective interaction J(1-z) (mean field approach). We extend the present formalism to include long-range interaction in the antiferromagnetic one-dimensional Heisenberg frustrated model and verify the absence of magnetic order for p>1 (where p is the decay interaction parameter, i.e., Jn=J/np). We also study the thermodynamic properties of the quenched decorated diluted Ising model with competitive interactions, using the differential operator technique with the effective field. The decorated Ising model with competitive interactions used is herein to describe the magnetic properties of the copper-oxide plane containing superconductor compounds in the insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (JA<0) with their nearest-neighbors, and ferromagnetically (JF>0) with the quenched spins that decorate the bonds (simulating the Cu-O interaction), and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., ). Moreover, in our model some magnetic sites (atoms of Cu) are substituted by non-magnetic sites. We study the thermodynamic properties of the system and the limit of antiferromagnetic stability in the phase diagrams (T,p) and (T,z), for some values of the frustration parameter (α= J ' = λ ,λ = 10−5 A A J J A\JF) and magnetic field. We observe for some values α, the system presents a reentrant behavior in low temperatures, which also is reflected in the thermodynamic properties.