Previously, we have presented a methodology to extend canonical Monte Carlo methods inspired on a suitable extension of the canonical fluctuation relation $C=beta^{2}<delta E^{2}>$ compatible with negative heat capacities $C<0$. Now, we improve this methodology by introducing a better treatment of finite size effects affecting the precision of a direct determination of the microcanonical caloric curve $beta (E) =partial S(E) /partial E$, as well as a better implementation of MC schemes. We shall show that despite the modifications considered, the extended canonical MC methods possibility an impressive overcome of the so-called textit{super-critical slowing down} observed close to the region of a temperature driven first-order phase transition. In this case, the dependence of the decorrelation time $tau$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $tau(N)propto N^{alpha}$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $alpha=0.14-0.18$.
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