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.

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In this work we use a refined entropic sampling technique based on the Wang-Landau method to study the spin-1/2 Baxter-Wu model. The static critical exponents were determined as α = 0.6545(68), β = 0.0818(30), γ = 1.18193(77), and ν = 0.66341(47). The estimate for the critical temperature was Tc = 2.269194(45). We compare the present results with those obtained from other well established approaches and we find a very good closeness with the exact values, besides the high precision reached for the critical temperature. We also calculate the coefficients a and b for the divergence of the microcanonical inverse temperature at the ground state achieving an excellent agreement in comparison with the simulation estimates.

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