Universality aspects of the two-dimensional spin-1 Baxter-Wu model in a crystal field

We investigate the universality aspects of the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field. We employ Wang-Landau entropic sampling simulations and a detailed finite-size scaling analysis at the regime of second-order phase transitions of the phase diagram that allows the estimation of the critical exponents $\nu$, $\alpha$, and $\gamma$, as well as the the universal ratio of the correlation length over the linear size of the system $\xi/L$. Our results clearly indicate that the transition belongs to the universality class of the corresponding spin-1/2 model and therefore to the universality class of the $q = 4$ Potts model.