We investigate the critical behavior of the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal-field coupling Δ with the goal of determining the universality class of transitions along the second-order part of the transition line as one approaches the putative location of the multicritical point. We employ extensive Monte Carlo simulations using two different methodologies: (i) a study of the zeros of the energy probability distribution, closely related to the Fisher zeros of the partition function, and (ii) the well-established multicanonical approach employed to study the probability distribution of the crystal-field energy. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram supports previous claims that the transition belongs to the universality class of the four-state Potts model. For positive values of Δ, we observe the presence of strong finite-size effects, indicative of crossover effects due to the proximity of the first-order part of the transition line. Finally, we demonstrate how a combination of cluster and heat-bath updates allows one to equilibrate larger systems, and we demonstrate the potential of this approach for resolving the ambiguities observed in the regime of Δ≳0.
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.
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=1 and spin
S=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=1, while an isolated double-critical-endpoint is present for spin
S=3/2. Although the topology of the phase diagram of the Baxte-Wu model for spin
S=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=3/2 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 two-dimensional Baxter-Wu model with spin-1, in the presence of a crystal field, is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. Single histogram techniques are used to get the results close to the phase transitions. The finite-size scaling procedure is employed in order to obtain the critical behavior. The simulations have shown that the critical exponents are different from the spin-1/2 case and are crystal field dependent.