Multicanonical simulations of the 2D spin-$1$ Baxter-Wu model in a crystal field

We investigate aspects of universality in the two-dimensional (2D) spin-$1$ Baxter-Wu model in a crystal field $\Delta$ using a parallel version of the multicanonical algorithm employed at constant temperature $T$. A detailed finite-size scaling analysis in the continuous regime of the $\Delta-T$ phase diagram of the model indicates that the transition belongs to the universality class of the $4$-state Potts model. The presence of first-order-like finite-size effects that become more pronounced as one approaches the pentacritical point of the model is highlighted and discussed.