Propriedades termodinâmicas de sistemas magnéticos frustrados - Griffith Mendonça Andrade Sousa (2013)
In this work, we present some thermodynamic properties of the anisotropic Heisenberg model with antiferromagnetic interactions in two and three dimensions. First, we study the zero temperature properties of the two-dimensional spatially anisotropic ferrimagnet with competing interactions, using the linear spin-wave theory, and considering pairs of mixed-spins in the set (1/2,1,3/2). For some values of the anisotropy parameter, we find a small region magnetically disordered in the phase diagram. Using a modified spin wave theory, the ordered phases of the two dimensional S=1 antiferromagnet with next and near next neighbor exchange interactions and easy axis single ion anisotropy on the square lattice are studied. We calculate the phase diagram at T = 0, and some thermodynamic quantities at finite temperatures. In the final part of the thesis, we use the bond operator technique to study the antiferromagnetic Heisenberg model with spin S=1 with easy plane anisotropy. We study the effects of frustration between nearest, next-nearest neighbor and next-next-nearest neighbors (NNN) of the quantum S=1 anisotropic antiferromagnetic Heisenberg model on a simple cubic lattice with single ion anisotropy. We calculate the phase diagram at zero temperature and the gap as a function of temperature in the disordered paramagnetic phase. Finally, we study the cubic lattice with interaction between nearest neighbors and a coupling between planes. We have considered an in-plane single ion anisotropy D and an intra-plane anisotropy Dx. Applying an external magnetic field h in the z direction, we calculate: i) the magnetization m in the direction of the field. ii) the magnetization mx in the plan perpendicular to the z axis. Our results indicate that the anisotropy Dx reduces mx and critical temperature Tc, while y and h induce long-range order in the system.