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Journal of Physics Conference Series

Universality and phase diagrams of the Baxter-Wu Model in a Crystal Field: spin-1 and spin-3/2

Daniele Alves Dias, J. C. Xavier, J. A. Plascak

Published Nov 1, 2017• 0 citations
Publisher

Abstract

Conventional finite-size scaling and conformal invariance theory are used in order to study the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model. For spin-1 the results are similar to the Blume-Capel model. However, for spin-3/2, the phase diagram is much richer, and presents, besides a pentacritical point, an additional multicritical endpoint. In both cases, the universality class is the same as the spin-1/2 model, even at the multicritical points.

DOI
10.1088/1742-6596/921/1/012003

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Conventional finite-size scaling and conformal invariance theory are used in order to study the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model. For spin-1 the results are similar to the Blume-Capel model. However, for spin-3/2, the phase diagram is much richer, and presents, besides a pentacritical point, an additional multicritical endpoint. In both cases, the universality class is the same as the spin-1/2 model, even at the multicritical points.
The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.
The phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field in two dimensions is explored by renormalization group, conventional finite-size scaling, and conformal invariance techniques. We found that the phase diagram of this model is qualitatively the same as that of the dilute 4-states Potts model, presenting a multicritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. However, our results indicate that the critical exponents vary continuously along the second-order transition line, differently from the expected behavior of the dilute 4-states Potts model.
We have studied the critical, multicritical and first order behavior of the Spin-1 Baxter-Wu model in a crystal field. We have employed the mean field renormalization group approach and extensive Monte Carlo simulations using the single spin flip Metropolis algorithm and hystogram techniques. The global phase diagram is obtained and it is shown that the system belongs to the same universality class as the corresponding spin-1/2 version and presents a multicritical point separating a second order phase transition line from a first order line. The probability distribution of this pentacritical point is also determined.
We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.
The Blume-Capel model on a square lattice and the Baxter-Wu model on a triangular lattice have been studied through extensive Monte Carlo simulations using the single spin update according to the Metropolis algorithm. Both models have been treated with spin S=1S=1S=1 and spin S=3/2S=3/2S=3/2 in the presence of crystal field interactions. The transition temperature and correlation length critical exponent have been computed, as a function of the crystal field interaction, by employing the recent developed method of the zeros of the energy probability distribution. The important question of the universality class along the second-order transition lines could be resolved by looking at the corresponding universal probability distributions of the energy and magnetizations. Mixing field arguments turned out to be quite important to decide the possible change in the universality class of the models as the crystal field varies. Single histograms techniques have also been utilized in order to obtain simulational data close to the second-order transitions and multicritical points. As expected, the Blume-Capel model has first- and second-order transitions, where a tricritical point occurs for spin S=1S=1S=1, while an isolated double-critical-endpoint is present for spin S=3/2S=3/2S=3/2. Although the topology of the phase diagram of the Baxte-Wu model for spin S=1S=1S=1 is similar to that of the Blume-Capel model, with the tricritical point being replaced by a pentacritical point, the Baxter-Wu model has critical exponents that change along the tetracritical line as the crystal field is increased. On the other hand, the Baxter-Wu model with spin S=3/2S=3/2S=3/2 has a phase diagram that is completely different from the one obtained for the Blume-Capel, with the presence of a pentacritical point and a tetracritical endpoint. The present data also show that, despite the change of the probability distributions as the crystal field varies, the models with different spin values belong to the same universality class.
The phase diagram of the spin-32\frac{3}{2}23​ Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance, and Monte Carlo simulations. The model in its $\ensuremath{\tau}$-continuum Hamiltonian version is also considered and compared with other spin-32\frac{3}{2}23​ quantum chains. Our results indicate that, different from the standard spin-1 Blume-Capel model, there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean-field prediction, but in disagreement with previous approximate renormalization-group calculations.