Simulações entrópicas do Modelo de Baxter-Wu
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2017-08-04
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Universidade Federal de Goiás
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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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Citação
JORGE, L. N. Simulações entrópicas do Modelo de Baxter-Wu. 2017. 107 f. Tese (Doutorado em Física) - Universidade Federal de Goiás, Goiânia, 2017.