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Generalized Metropolis dynamics with a generalized master equation : an approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

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Generalized Metropolis dynamics with a generalized master equation : an approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

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Título Generalized Metropolis dynamics with a generalized master equation : an approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems
Autor Silva, Roberto da
Felício, José Roberto Drugovich de
Martinez, Alexandre Souto
Abstract The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature β. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q=1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q ≠ 1, we showthat suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.
Contido em Physical review. E, Statistical, nonlinear, and soft matter physics. Vol. 85, no. 6 (June 2012), 066707, 9 p.
Assunto Análise numérica
Energia livre
Equação de Boltzmann
Equacao master
Mecânica estatística
Método de Monte Carlo
Sistemas de spin
Origem Estrangeiro
Tipo Artigo de periódico
URI http://hdl.handle.net/10183/101874
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