On the order of the phase transition in the spin-1 Baxter–Wu model

Abstract

In this work we investigate the order of the phase transition of the spin-1 Baxter-Wu model. We used extensive entropic simulations to describe the behavior of quantities which reveal the order of the phase transition. We applyied finite-sizing scaling laws for continuous and discontinuous phase transitions. Our results show that this system exhibits an indeterminacy regarding the order of the phase transition, i.e., the results are conclusive for both transitions, whether continuous or discontinuous. In such a scenario we carried out a study of the configurations in the region of the phase transition, which confirmed that the model seems to undergo a tetracritical transition, with the coexistence of a ferromagnetic and three ferrimagnetic configurations, suggesting that it may be a multicritical point belonging to a critical line of an external or a crystalline fields, where the continuous and the discontinuous phase transitions may coexist reflecting different features of the system.

An entropic simulational study of the spin-$1$ Baxter-Wu model in a crystal field

“…However, this double peak characteristic can be a finite-size effect and, a more detailed study in this region is still missing. For positive values of the field, the finite-size effect will not remove the two peaks, since we have for the case D = 0.0 the presence of these two peaks at the thermodynamic limit [10] and one can see that the greater the crystal field, the larger the separation between the two peaks. Therefore, we might conclude that the secondorder critical line is a line of tetracritical points.…”

“…Ref. 24 demonstrated that when using the order parameter as the total magnetization, one can consider systems with non-multiple of three lattice sizes without loss of generality of the model [10]. Thus we ran simulations for L = 8, 10, 14, and 16 with n = 24, 20, 20, and 16 independent runs, respectively.…”

“…1 shows, all maxima are very close to each other, around the same temperature, thereby a finite-size scaling behavior is not visible to the eyes. In fact, finite-size scaling effects for the critical temperature are very subtle when one uses lattice sizes that are not multiples of three [10,16,24]. Thus, the difference between the critical temperature at the thermodynamic limit and those obtained for the finite sizes is small, making the critical line observed in the diagram very close to that expected for an infinite system.…”

“…The case with D = 0 was studied using entropic simulations, resulting in the observation that the BW model presents a mixture of phase transitions [10], related to a tetracritical point. That was settled after the analysis of the energy probability, the configurations in the critical region, and by separating the density of states in two parts, sorting out the ferromagnetic and ferrimagnetic arrangements.…”

“…Entropic simulations [11][12][13][14] are excellent to study phase transitions and critical phenomena. The results obtained by this technique have revealed important characteristics regarding different models [10,[15][16][17]. The estimation of the joint density of states [14,17,18] brings a range of additional information, besides making it possi-ble to obtain thermodynamic properties for any temperature and coupling constants, allowing the construction of the phase diagram.…”