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In this work we use a refined entropic sampling technique based on theWang-Landau method to study the spin-$1/2$ Baxter-Wu model. The static criticalexponents were determined as $\alpha=0.6545(68)$, $\beta=0.0818(30)$,$\gamma=1.18193(77)$, and $\nu=0.66341(47)$. The estimate for the criticaltemperature was $T_c=2.269194(45)$. We compare the present results with thoseobtained from other well established approaches and we find a startlingcloseness with the exact values, besides the high precision reached for thecritical temperature. We also calculate the coefficients $a$ and $b$ for thedivergence of the microcanonical inverse temperature at the ground stateachieving an excellent agreement in comparison with the simulation estimates.

Critical behavior of the spin-$1/2$ Baxter-Wu model: Entropic sampling simulations