Analyzing the accuracy and performance of the Wang-Landau algorithm for calculating the density of states in the Ising model

We analyzed the accuracy and performance of the Wang-Landau algorithm in calculating the density of states for the two-dimensional Ising model. Our findings indicate that calculating the density of states simultaneously by energy and magnetization enhances the accuracy of energy moment estimations. As the lattice size increases, the relative error in the density of states decreases. However, for large lattices, it is not possible to estimate the execution time of the algorithm in advance, as the criterion for switching to the $1/t$ mode is never met.