Extending canonical Monte Carlo methods

Abstract

In this paper, we discuss the implications of a recently obtained equilibriumfluctuation-dissipation relation for the extension of the available Monte Carlomethods on the basis of the consideration of the Gibbs canonical ensemble toaccount for the existence of an anomalous regime with negative heat capacitiesC < 0. The resulting framework appears to be a suitable generalization of the methodologyassociated with the so-called dynamical ensemble, which is applied to the extension of twowell-known Monte Carlo methods: the Metropolis importance sampling and theSwendsen–Wang cluster algorithm. These Monte Carlo algorithms are employed to studythe anomalous thermodynamic behavior of the Potts models with many spin statesq definedon a d-dimensional hypercubic lattice with periodic boundary conditions, whichsuccessfully reduce the exponential divergence of the decorrelation timeτ with increase ofthe system size N to a weak power-law divergence with α≈0.2 for the particular case of the 2D ten-state Potts model.