Extending canonical Monte Carlo methods II

Abstract

Previously, we have presented a methodology to extend canonical Monte Carlo methods inspired on a suitable extension of the canonical fluctuation relation $C=β^{2}<δE^{2}>$ 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 $β(E) =\partial S(E) /\partial E$, 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 $τ$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $τ(N)\propto N^α$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $α=0.14-0.18$.

Version submitted to JSTAT