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Register a new userExtended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique
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Added by
Luisberis Velazquez-Abad
Publication date
2016
fields
Physics
and research's language is
English
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Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application a re-weighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multi-histograms method of Ferrenberg and Swendsen. As example of application, we reconsider the study of four-state Potts model on the square lattice $Ltimes L$ with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site $q_{L}$ during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power-law $q_{L}(L)propto(1/L)^{z}$ with exponent $zsimeq0$.$26pm0$.$02$. It is discussed the compatibility of these results with the continuous character of temperature-driven phase transition when $Lrightarrow+infty$.
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In this work, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation on the extension of the available Monte Carlo methods based on the consideration of the Gibbs canonical ensemble to account for the existence of an anomalous regime with negative heat capacities $C<0$. The resulting framework appears as a suitable generalization of the methodology associated with the so-called textit{dynamical ensemble}, which is applied to the extension of two well-known Monte Carlo methods: the Metropolis importance sample and the Swendsen-Wang clusters algorithm. These Monte Carlo algorithms are employed to study the anomalous thermodynamic behavior of the Potts models with many spin states $q$ defined on a $d$-dimensional hypercubic lattice with periodic boundary conditions, which successfully reduce the exponential divergence of decorrelation time $tau$ with the increase of the system size $N$ to a weak power-law divergence $taupropto N^{alpha}$ with $alphaapprox0.2$ for the particular case of the 2D 10-state Potts model.
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