Sistemas magnéticos com interações competitivas: uma abordagem de campo médio com clusters

Abstract

We study a model of localized spins which can assume three different states, S = 0 and 1, with two competing interactions: a antiferromagnetic first neighbour interaction (JA) and a three body interaction between third neighbours (JB), occurring only when there is a site in with S = 0 between the interacting states. We also consider a crystal field (D), which favors the states S = 0 when D < 0 and S = 1 when D > 0. We treated this model in a cluster mean-field approximation, which reduces a many-body problem to a effective single cluster one. In which, through Bogoliubov’s inequality, we use a variational principle to obtain an approximation to the free energy. Analyzing the behavior of the free energy and the order parameters, we can mark and characterize the phase transitions, allowing us to construct phase diagrams of the temperature by the third neighnour interaction and by the crystal field for different cluster sizes. From the analysis of the T=jJAj JB=jJAj phase diagram, we found that the competition between the first and third neighbor interaction is maximum at JB=jJAj = �����2, where the antiferromagnetic and super antiferromagnetic phases coexist at T = 0. Furthermore, our studies, through the analysis of the T=jJAj D=jJAj phase diagrams, demonstrate that incorporating clusters in the approach leads to a significant improvement in the obtained results when compared to the usual mean-field approach. Our cluster results also show the emergence of a new type of order in the system, called cluster antiferromagnetic, characterized by nonzero magnetizations in a square plaquette. In our analysis we shown that this order is a mixture of different microscopic states with non magnetic sites, which can difficult its characterization in Monte Carlo simulations. Another aspects in which the cluster approach improves the results is in the characterization of the phase transitions between the antiferromagnetic and paramagnetic phases. In particular, we hope that our investigation will motivate further studies of this model, considering different analytical and numerical methods