In this paper, we investigate the thermodynamic properties of an Aharonov-Bohm (AB) quantum ring in a heat bath for both relativistic and non-relativistic cases. For accomplishing this, we used the partition function which was obtained numerically using the Euler-Maclaurin formula. In particular, we determined the energy spectra as well as the behavior of the main thermodynamic functions of the canonical ensemble, namely, the Helmholtz free energy, the mean energy, the entropy and the heat capacity. The so-called Dulong-Petit law was verified only for the relativistic case. We noticed that in the low energy regime, the relativistic thermodynamic functions are reduced to the non-relativistic case as well.

We investigate the presence of vortex structures in a Maxwell model with a logarithmic generalization. This generalization becomes important because it generates stationary field solutions in models that describe the dynamics of a scalar field. In this work, we will choose to investigate the dynamics of the complex scalar field with the gauge field governed by the Maxwell term. For this, we will investigate the Bogomol'nyi equations to describe the static field configurations. Then, we show numerically that the complex scalar field solutions that generate minimum energy configurations have internal structures. Finally, assuming a planar vision, the magnetic field and the density energy show the interesting feature of the ring-like vortex.

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The thick brane scenario built on the f (T, B) teleparallel gravity theory was considered for the study of phase transitions, internal structures and new classes of solutions in a model. In this theory, T denotes the torsion scalar, and B is a boundary term. An interesting result was observed when brane splitting occurs, i. e., internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multi-kink) so that for appropriate values of the parameters k 1,2 multiple phase transitions are identified. To perform this analysis, the Differential Configurational Entropy (DCE) that has the ability to predict the existence of phase transitions through critical points was used. Furthermore, the DCE is able to select the most stable solutions since it gives us details about the informational content to the field settings.

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