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

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. 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 not equal 1, we show that 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.

A theoretical study of SnF2+, SnCl2+, and SnO2+ and their experimental search

We present a detailed theoretical study of the stability of the gas-phase diatomic dications SnF2+, SnCl2+, and SnO2+ using ab initio computer calculations. The ground states of SnF2+, SnCl2+, and SnO2+ are thermodynamically stable, respectively, with dissociation energies of 0.45, 0.30, and 0.42 eV. Whereas SnF2+ dissociates into Sn2+ + F, the long range behaviour of the potential energy curves of SnCl2+ and SnO2+ is repulsive and wide barrier heights due to avoided crossing act as a kind of effective dissociation energy. Their equilibrium internuclear distances are 4.855, 5.201, and 4.852 a(0), respectively. The double ionisation energies (T-e) to form SnF2+, SnCl2+, and SnO2+ from their respective neutral parents are 25.87, 23.71, and 25.97 eV. We combine our theoretical work with the experimental results of a search for these doubly positively charged diatomic molecules in the gas phase. SnO2+ and SnF2+ have been observed for prolonged oxygen (O-16(-)) ion beam sputtering of a tin metal foil and of tin (II) fluoride (SnF2) powder, respectively, for ion flight times of about 10(-5) s through a magnetic-sector mass spectrometer. In addition, SnCl2+ has been detected for O-16(-) ion surface bombardment of stannous (tin (II)) chloride (SnCl2) powder. To our knowledge, SnF2+ is a novel gas-phase molecule, whereas SnCl2+ had been detected previously by electron-impact ionization mass spectrometry, and SnO2+ had been observed before by spark source mass spectrometry as well as by atom probe mass spectrometry. We are not aware of any previous theoretical studies of these molecular systems. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758475]