Efeito de campos magnéticos aleatórios na rede de Ising triangular frustrada

Abstract

This dissertation aims to investigate the phenomenon of magnetization plateaus in the twodimensional triangular lattice antiferromagnetic Ising model, with emphasis on the combined effect of random and uniform magnetic fields. While the Ising model under a uniform magnetic field already predicts the existence of a plateau in the magnetization curve, we extend the analysis to consider the possible effects of random magnetic fields that mimic the effects of impurities acting locally on the lattice sites. The central question guiding this study is: to what extent can the randomness of local magnetic fields induce the emergence of new plateaus, modify existing ones, or, conversely, suppress the formation of these plateaus? To answer this question, we adopted a methodology based on the exact enumeration of the partition function for clusters of different lattice sizes (3, 6, 9, and 15 sites) and on the cluster mean-field approximation. The random magnetic fields were modeled using two discrete and symmetric probability distributions: the bimodal and the trimodal, chosen for their simplicity and analytical feasibility. We analyzed the fundamental magnetic properties, such as magnetization, magnetic susceptibility, and magnetic entropy, under the simultaneous influence of random magnetic fields and a uniform magnetic field. The results indicate that the disorder introduced by random magnetic fields can indeed contribute to the emergence of additional plateaus in the magnetization, fragmenting the existing plateaus. We observed that the number and position of these plateaus depend on both the probability distribution of the random fields and their intensity. Furthermore, we verified that the disorder significantly affects the thermodynamic quantities studied, particularly the magnetic entropy, which exhibited local maxima in the critical region of the plateaus. These findings suggest that random magnetic fields can be used as a mechanism for plateau fragmentation in magnetization, shedding light on the understanding of the combined effects of geometric frustration and disorder in the studied system. These results are promising for future studies, including extensions to the magnetocaloric effect, which, in the critical field region of the plateaus, exhibits local maxima in magnetic entropy, as well as for diluted antiferromagnetic systems with non-magnetic ions.