Extending canonical Monte Carlo methods II

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 $\beta (E)=\mathrm{\partial }S(E)\mathrm{/}\mathrm{\partial }E$, 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 $\mathit{\text{super-critical}}\mathit{\text{slowing}}\mathit{\text{down}}$ 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 $\alpha =0.14-0.18$.