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Velazquez and Curilef have proposed a methodology to extend Monte Carloalgorithms that are based on canonical ensemble. According to our previousstudy, their proposal allows us to overcome slow sampling problems in systemsthat undergo any type of temperature-driven phase transition. After acomprehensive review about ideas and connections of this framework, we discussthe application a re-weighting technique to improve the accuracy ofmicrocanonical calculations, specifically, the well-known multi-histogramsmethod of Ferrenberg and Swendsen. As example of application, we reconsider thestudy of four-state Potts model on the square lattice $L\times L$ with periodicboundary conditions. This analysis allows us to detect the existence of a verysmall latent heat per site $q_{L}$ during the occurrence of temperature-drivenphase transition of this model, whose size dependence seems to follow apower-law $q_{L}(L)\propto(1/L)^{z}$ with exponent $z\simeq0$.$26\pm0$.$02$. Itis discussed the compatibility of these results with the continuous characterof temperature-driven phase transition when $L\rightarrow+\infty$.

Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique