Extending canonical Monte Carlo methods II

TL;DR

This paper enhances extended canonical Monte Carlo methods by improving finite size effect treatments and implementation, significantly reducing critical slowing down near phase transitions, demonstrated on the 2D seven-state Potts model.

Contribution

It introduces a refined methodology for extended canonical Monte Carlo simulations, improving accuracy and efficiency near phase transitions.

Findings

Finite size effects are better handled, increasing precision.

Critical slowing down is reduced from exponential to power-law behavior.

Demonstrated on the 2D seven-state Potts model with a low exponent for decorrelation time.

Abstract

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 $\alpha=0.14-0.18$.