Frustrated model to describe reentrant behavior in copper oxide superconductors

The quenched decorated Ising model with competitive interactions is used here to described the magnetic properties of the copper oxide superconductors 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 spins that decorate the bonds, which are quenched and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., JA′=λJA, λ=10-5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T-p), for λ=10-5 and various values of frustration parameter α=JA/JF. For certain region range of the parameter α we observe a reentrant behavior at low-temperature. We also discuss the critical behavior of TN versus α for some values of decorated bond concentrations and reentrant phenomena is observed. We calculate the dependence of the staggered magnetization as a function of the temperature to analyze the reentrant behavior observed in the phase diagrams.