Banca de DEFESA: CHARLES SOUZA DO AMARAL
Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.STUDENT : CHARLES SOUZA DO AMARAL
DATE: 14/09/2021
TIME: 14:30
LOCAL: Videoconferência
TITLE:
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KEY WORDS:
Percolation Model; Ising Model; Multirange Percolation Model; Multirange Ising Model; Constrainded-degree Percolation Model; Phase Transition.
PAGES: 103
BIG AREA: Outra
AREA: Multidisciplinar
SUMMARY:
Percolation and Ising models have applications in several areas of science and are among the most studied models in Statistical Mechanics. They exhibit a phase transition and determining the critical value at which it occurs is one of the main issues related to these models. The aim of this work is to study three models, two percolation and one Ising, in which the critical value varies as a function of some parameter. The first model presented is the Multirange Percolation Model (MPM), in which we consider the classic model of percolation in the hypercubic lattice Ld and add bonds of sizes m1,m2,...,mn, parallel to each coordinate axis, so that the sizes of the larger bonds are multiples of the smaller ones, and mi > 1 for all i. There is an analytical result showing that the critical point of this model converges to that of the classical model in the hypercubic lattice Ld(n+1) when mi → ∞ for all i. We find numerical evidence that, if d = 2, this convergence is monotonous and follows a power law when n = 1 and n = 2. In order to verify whether the convergence related to the critical point in the MPM also occurs in other models that exhibit phase transition, we studied the Multirange Ising Model, which is defined similarly to the MPM. We verified that, if we analyze the critical temperature instead of the critical point, convergence will also occur for the same situations studied in the MPM. Finally, we also study the Constrained-Degree Percolation Model (CDPM). In it, we try to open the bonds of the graph in a random order that is previously defined. Each bond is opened if it satisfies a certain restriction that depends on a k parameter. This model has applications in the study of dimers and polymers and we simulate it in the hypercubic lattice Ld for d ∈ {2,3,4}. Through a numerical analysis, we show that the critical value of the model decreases as function of the constraint k. Furthermore, we found evidence that the CDPM is in the same universality class as the classical Ising model.
BANKING MEMBERS:
Externo à Instituição - RONALD DICKMAN - UFMG
Presidente - ALLBENS ATMAN PICARDI FARIA
Interno - ARTHUR RODRIGO BOSCO DE MAGALHAES
Externo à Instituição - BERNARDO NUNES BORGES DE LIMA - UFMG
Externo à Instituição - ROGER WILLIAM CÂMARA SILVA - UFMG
Interno - THIAGO GOMES DE MATTOS