Entropic simulations of the spin-1/2 Baxter-Wu model.

Among the various models used to describe spins systems the Baxter-Wu model is particularly interesting, since it considers triplets of spins, thus, it does not presents spin-reversal symmetry, as it occurs in the most know models. This model is defined in a triangular two-dimensional lattice, and the three-spin interaction is given by the Hamiltonian,
\begin{eqnarray}
H_{BW} = -J\sum_{<i,j,k>}s_{i}s_{j}s_{k},
\end{eqnarray}
where the variables of spin are located at the vertices of the triangular lattice and take the values $s_i=\pm1$, $J$ is the coupling constant that defines the energy scale and the sum extends over all the triangular faces. For the spin-$1/2$ case, the model was exactly solved by Baxter and Wu, and presents the same critical temperature of the Ising model, but the critical exponents are those of the $q=4$ Potts model, so, this model is an
excellent object of study to test new Monte Carlo procedures. Monte Carlo simulations are an efficient tool to calculate critical temperatures and static critical exponents. In particular, the Wang-Landau sampling has become in last years more and more accurate and robust. In this
work we present a simulational study of the pure spin-1/2 Baxter-Wu model using a modified Wang-Landau scheme to calculate the critical exponents $\gamma$, $\beta$ and $\nu$ and the critical temperature $T_c$ in the Baxter-Wu model. In this new procedure, instead of updating the density of states after every spin-flip we adopt the Monte Carlo sweep for updating the density of states, the microcanonical averages are accumulated only after a few Wang-Landau levels have already run out, and stop the simulations when a checking parameter, $\varepsilon$, which measures the fluctuation of the peak of the specific heat during the simulations, varies below $10^{-4}$ for a complete Wang-Landau level. As a result, different runs proceed up to different final modification factors. Moreover, the final results are obtained as averages over ten independent sets of finite size scaling simulations. Our results are very consistent and we compare them with exact data available in literature.