Modelo de Heisenberg diluído: nova teoria de campo efetivo

Abstract

The critical properties of quantum spin systems is one of the most fascinating subjects in solid physics. Especially, extensive studies have been made in the spin-1/2 Heisenberg antiferromagnetic model (HAM) because the undoped cuprates contain two-dimensional Cu-O planes antiferromagnetic (AF) interactions. Anderson s original suggestion that novel quantum spin fluctuations in the CuO2 planes, common in all these doped cuprates,may be responsible for the superconductivity has recieved significant attention. Most studies on the HAM have focused by analysing the properties on ground state (T=0) on a square lattice, where conclusion has been that the isotropic HAM is in an ordered state, with a nonzero staggered magnetization, corresponding to a spontaneously broken symmetry. On the other hand, the phase transition of the spin-1/2 anisotropic Heisenberg ferromagnetic Model (HFM), that obtain direct information about the critical exponents and critical temperature, has been globally analyzed by many methods. For a not frustrated classical system and some quantum system (e.g., the XY model), there is a unitary operator in which the F case is simply mapped into the AF case by redifining the spin direction on one sublattice (J display by -J, where J is the exchange coupling), in lattices that are decomposed into two sublattices, to which we limit ourselves presently, but for the general quantum Heisenberg model no such symmetry exists. Recently, the effective field theory (EFT) method have been applied successfully to study a large variety of problems, in particular quantum models in arbitrary dimension and it is able to study frustrated models. The starting point for the EFT calculation is the choice of a finite cluster and obtain average of spin operators by using the Callen and Suzuki generalized relation. The EFT provides a hyerarchy of approximations to vii obtain thermodynamic properties of magnetics models. On can continue this series of approximations to consider larger and larger clusters and as a consequence, better results are obtained. The exact solution would be obtained by considering an infinite cluster. However, by using relatively small clusters that contain the topology of the lattice, one can obtain a reasonable description of thermodynamic properties. Here we use EFT in finite cluster to treat the Heisenberg antiferromagnet with dilution bond and obtain the phase diagram in the T-p plane (p is probability of bond). We develpod a new decouling in the correlation equations generated by formalism.