# Efficient Wang-Landau Sampling for the Baxter-Wu Model

This study analyzes the two-dimensional Baxter-Wu model of Spin-1/2 and Spin-1 through the revenue to improve the accuracy of the Wang-Landau sampling. This scheme of Wang-Landau was proposed by Caparica and Cunha-Neto[1]. Remembering that Wang-Landau simulation primordial [2] generates the density of states $g(E)$, i.e. the number of all possible states (or configurations) for any energy level E of the system, allowing determine the canonical average of any thermodynamic variable, as $<X>_T = \frac{\sum_{E}<X>_{E}g(E) e^{-\beta E}}{\sum_{E} g(E)e^{-\beta E}}$, where $<X>_{E}$ is the microcanonical average accumulated during the simulations and $\beta = 1/k_{B} T$ , $k_{B}$ is the Boltzmann constant and T is the temperature. Our analysis accomplish the two approaches of Wang-Landau: the conventional (WLS) and the improved precision (MWLS) for the Baxter-Wu model, where we observe the behavior of the temperature of the maximum of the specific heat and magnetic susceptibility as a function of the Monte Carlo sweeps (MCS) , where update the density of states only after every spin-flip (WLS), and update it after each Monte Carlo sweep (MWLS) and, in the case susceptibility, the MWLS shows that there is a limit to begin the accumulation the microcanonicas media. This study also showed the density of states for the Baxter-Wu Spin-1/2 and Spin-1, and perform a scale analysis of finite size for the model.

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[1] A. A. Caparica and A. G. Cunha-Netto, Phys. Rev. E 85, 046702.

[2] Fugao Wang and D. P. Landau Phys. Rev. Lett. 86, 2050.