Programa de Pós-graduação em Física

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Navegando Programa de Pós-graduação em Física por Por Orientador "Caparica, Álvaro de Almeida"

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    Simulações entrópicas do modelo de Ashkin-Teller
    (Universidade Federal de Goiás, 2016-03-10) Ferreira, Lucas de Souza; Caparica, Álvaro de Almeida; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4788151Z6; Caparica, Álvaro de ALmeida; Branco, Nilton da Silva; Bufaiçal, Leandro Felix de sousa
    In 1943, Ashkin and Teller (AT) proposed a model to describe the behavior of a system composed by four components that interact with each other. However the problem has not been solved analytically for all parameters due to the complexity of the model. Only thirty years later Fan (1972) proposed a change in order to analyze the system. He made an analogy with the Ising model and described the interactions between the components in terms of spins, leading to a simple matching with the Ising and Potts q = 4 models and, enabling therefore a clearer comprehension of the model and allowing the implementation of various techniques to investigate the behavior of the system with the temperature. In 2001 Wang and Landau developed a Monte Carlo algorithm that estimates directly the density of states and can be applied in the study of phase transitions and the thermodynamic properties. This algorithm is based on a random walk in the space of energies that leads to an estimate for the density of states. During the simulations an energy histogram monitors the evolution of the density of states: whenever the flatness criterion is satisfied, we obtain a finer level of the density of states. In this work we perform a study of the Ashkin-Teller model using the Wang-Landau algorithm, determining the behavior of the magnetization and the specific heat and estimating the critical exponents , and and the critical temperature through the finite-size theory for different values of the model parameters.
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    Simulações entrópicas do modelo de Bell-Lavis para a água
    (Universidade Federal de Goiás, 2020-04-07) Ferreira, Lucas de Souza; Caparica, Álvaro de Almeida; http://lattes.cnpq.br/4726638254587108; Caparica, Álvaro de Almeida; Rabelo, José Nicodemos Teixeira; Bakuzis, Andris Figueiroa; Chahine, Jorge; Barbosa, Marco Aurélio Alves
    In this work we used the entropic sample simulation to study the Bell-Lavis model for the liquid water. We estimed the joint density of states with which we obtain the average of the termodynamic properties of the energy, specific heat, density of particles, hydrogen bond energies, and the susceptibility of the density of particles to many values of the constants H and μ. Through of the analyze of this quantities we determined the possible ground states and the values for H and μ for which happen the transition between the ground states. We observe that for H = 1, 0 and 0, 0 < μ < 0, 5 the density of particles shows a maximum associated to transition from a configuration of low density to a configuration of high density. In this range the specific heat show two maxima, the first associated to maximum in the density, and do not shows finite size effects , and the second a transition order disorder. For 0.5 < μ < 1.5 we have only one maximum for the specific heat which is the fusion of the two before. We performed a finite size scaling study for μ = 1, 0 observing the thermodynamic quantities that characterize a second order fase transition and we found a critical temperature Tc = 0, 510718(49), while when observing the thermodynamic quantities that characterize a first order fase transition we obtain Tc = 0, 564520(37). Such results indicate the presence of two orders of phase transitions at very close temperatures. For understand the behavior we analise the order parameter to the one dimensional Ising model and conclude that the right choice of the order parameter for the model is decisive to visualize the phase transition. For the Bell-Lavis model the choice of this parameter is yet a challenge to be overcome.
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    Simulações entrópicas do Modelo de Baxter-Wu
    (Universidade Federal de Goiás, 2017-08-04) Jorge, Lucas Nunes; Caparica, Álvaro de Almeida; http://lattes.cnpq.br/4726638254587108; Sousa, José Ricardo de; Godoy, Maurício; Vale, Renato Pessoa; Silva, Hermann Freire Ferreira Lima e
    In this work, we used a refined entropy sampling technique based on the Wang- Landau method and finite-size scaling techniques to study variations of the Baxter-Wu model, namely: spin-$1/2$, spin-$1$, spin-$1$ with the crystal field interaction and was done a three-dimensional proposal for the model. It was also verified characteristics in the order parameter to be adopted in the simulations. The universality class and the critical temperature were calculated for the spin-$1/2$ case, and the results founded were in good agreement with the exact ones found in the literature. We sought to determine the kind of the phase transition that the model suffers for the spin-$1$ case, being carried out a detailed study for continuous and discontinuous phase transitions. The Baxter-Wu model with crystal field, $D$, had its phase diagram constructed, as well as the determination of the point at which discontinuous transitions finalizes. The critical exponent, $\nu$, was evaluated for several values of the crystal field, where we verified is variation along the critical line, with the existence of a peak, corroborating the existence of a multicritic behavior of the model. We also observed the existence of an anomaly in the specific heat, associated to the Schottky defect. This anomaly appears more clearly for values of $D \geq 1.990$. In the study of the order parameter, we verified that in the simulations one should not, when considering lattice sizes multiple of three, use the order parameter as the total magnetization of the lattice, but to consider the magnetization by sub-lattices. When working with sizes of lattices that are not multiples of three, it is not a problem to adopt the order parameter as the total magnetization of the lattice. A three-dimensional proposal was also made for the Baxter-Wu model, and its phase transition was characterized.
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    Frustração magnética em um modelo de ising triangular com anisotropia rotacional
    (Universidade Federal de Goiás, 2020-03-16) Nascimento, Ricardo Mayckon Lopes; Silva, Cláudio José da; http://lattes.cnpq.br/1361379226289069; Caparica, Álvaro de Almeida; http://lattes.cnpq.br/4726638254587108; Caparica, Álvaro de Almeida; Silva, Hermann Freire Ferreira Lima e; Branquinho, Luis Cesar
    In this work, we present a new model for the study of frustrated magnetic systems proposed for a triangular lattice equipped with Ising type spins that takes into account not only the interaction between the spins but also the interaction due to the symmetry of a given substrate that corresponds to a host lattice of the magnetic system. This last interaction is related to a phenomenological parameter that is responsible for controlling the intensity of this interaction and that is proportional to a function representative of the symmetry of the host material in question. The interest behind this study seeks to characterize the influence of this interaction on the behavior of the spins through the evaluation of their main thermodynamic properties associated with a phase transition that imply a new way of modeling these systems pointing to a complementary view of what can promote frustration in magnetic systems in general. For the development of this research, we adopted entropic sampling simulations based on the Wang-Landau method, where a random walk in the energy space is performed, allowing to estimate the density of states g(E) while the energy distribution is generated in the histogram. Through this methodology, we calculated some thermodynamic properties of interest and managed to represent a phase diagram that illustrates the various forms that the system takes in function of a control parameter that is responsible for adjusting the different magnetic phases of the model. We also adopted the finite-size scale theory that allowed us to estimate the critical exponents corresponding to a certain class of universality that the system may belong to. As a result of this, we were able to establish the proper conclusions regarding the dynamics of the system and we became able to formulate the possible developments resulting from this work.
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    Simulações entrópicas para um modelo tipo ZGB dependente da temperatura
    (Universidade Federal de Goiás, 2019-04-04) Santos, Eder Dourado dos; Caparica, Álvaro de Almeida; http://lattes.cnpq.br/4726638254587108; Caparica, Álvaro de Almeida; Sabino, José Ricardo; Silva, Claudio José da
    The ZGB model is a simple model built to describe some known steps of the CO−O2 reaction on a catalytic surface, which is represented in the model by a square lattice of side L. The main events that occur are the adsorption of monoxide molecules CO and O2 oxygen at empty sites of the lattice, which occur, respectively, with probabilities y and 1−y . Another important event is the formation of a molecule of carbon dioxide CO2 , which occurs whenever a molecule of CO and an atom O are first neighbors adsorbed in the lattice. Since an oxygen atom or a molecule of CO are adsorbed into the lattice, they remain in the sites coming out only by reactions. We propose a catalytic system saturated by CO molecules in order to study the effect of temperature on the system and the oxidation of these species using the rules of the model ZGB with small modifications. Attractive interactions between adsorbed CO molecules and O atoms at the first neighboring sites and the desorption phenomenon were taken into consideration. We consider the interaction CO-CO more intense than O-O , so that the system energy is minimal when the entire lattice is filled by CO molecules and is maximum when the lattice is empty or filled totally or partially by not near-neighbors CO and O, being null its value for all these cases. We perform a random walk in the energy space bounded by the interval above, calculating the density of states by means of entropic simulations. Once the state density is obtained, we calculate the partition function and the thermodynamic properties for a given temperature range by means of the canonical average. We found, through of a finite-size scale analysis, that our system suffers a first-order phase transition.
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    Simulações entrópicas do modelo de Baxter-Wu unidimensional
    (Universidade Federal de Goiás, 2020-06-10) Sousa, Rhayson Almeida de; Ferreira, Lucas de Souza; http://lattes.cnpq.br/4466090943358658; Caparica, Álvaro de Almeida; http://lattes.cnpq.br/4726638254587108; Caparica, Álvaro de Almeida; Bufaiçal, Leandro Felix de Sousa; Adão Neto, Minos Martins
    The Baxter-Wu model was initially proposed in 1972 by D. W. Wood and H. P. Griffiths and solved exactly by R. Baxter and F. Wu. The model is defined in a two-dimensional triangular lattice that can be decomposed into three triangular sub-lattice, so that any triangular face contains a spin from each sub-lattice at each vertex. The ground state of the model is four times degenerate, being formed by the positive ferromagnetic phase and three ferrimagnetic phases. The model also has a proposal for a three-dimensional lattice made by L. N. Jorge, L. S. Ferreira and A. A. Caparica inspired by the two-dimensional lattice, the ground state being only formed by the ferromagnetic phase and has a discontinuous order-disorder transition. The Baxter-Wu model of one-dimensional lattice was proposed by M. F. Calvacante and J. A. Plascak in the study of the Baxter-Wu model in different dimensionalities of lattices through the mean-field approach, where it presented a discontinuous order-disorder transition. In this work we studied the one-dimensional Baxter-Wu model using state counting and entropic simulations. We calculated the thermodynamic properties for different field and temperature values and obtained the ground state settings for three different regions that are separated at H = 0 and H = −3. Only on the interfaces we found out a finite size effect and a finite size study was performed for H = 0, obtaining the critical temperature and the critical exponents.