Ziya Merdan

The effect of the increase of linear dimensions on exponents obtained by finite-size scaling relations for the six-dimensional Ising model on the Creutz cellular automaton

The six-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4=

Effect Of The Number Of Energy Levels Of A Demon For The Simulation Of The Four-Dimensional Ising Model On The Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton by using three- and four-bit demons. The simulations result in overlapping curves for both the order parameter, the magnetic susceptibility, the internal energy and the Binder cumulant. However, the specific heat curves overlap above and at Tc as the number of energy levels of a demon or the number of bits increases, but below Tc they are strongly violated. The critical exponents for the order parameter and the magnetic susceptibility as the number of bits increases are obtained by analyzing the data according to the finite-size scaling relations available.

THE EFFECT OF THE INCREASE OF LINEAR DIMENSIONS ON EXPONENTS OBTAINED BY FINITE-SIZE SCALING RELATIONS FOR THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4 ≤ L ≤ 22. The exponents in the finite-size scaling relations for the order parameter, the magnetic susceptibility at the finite-lattice critical temperature and the specific heat at the infinite-lattice critical temperature are computed to be β = 0.5072(58), γ = 1.0287(56) and α = -0.096(17), respectively, which are consistent with the renormalization group prediction of β = 0.5, γ = 1 and α = 0. The critical temperatures for the infinite lattice are found to be

Computation of the Fractal Pattern in Manganese Dendrites

T_c^{chi}=6.6824(5)

Calculation of generalized elliptic type integrals using the binomial expansion theorem

and

Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons

T_c^C=6.6736(27)

The finite-size scaling study of four-dimensional Ising model in the presence of external magnetic field

, which are also consistent with the precise results.

The Simulation of the Two-Dimensional Ising Model on the Creutz Cellular Automaton for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

The images of manganese flowers (clusters) on the surface of the natural magnesium silicate substance are scanned and the pictures of them are transferred to computer atmosphere. By using these scanning parameters, the exponents of density correlation function and fractal dimension values are calculated. For all different groups between the least and the most dense in the samples, the correlation function exponents may range from 0.141 to 0.178 and the fractal dimension values may vary between 1.61 and 1.88. In addition, the manganese flowers are divided into seven different groups according to their smallest- and largest-density features. The formation of the natural manganese clusters (flowers, dendrites) on the surface of the magnesium silicate substance can be defined by using the deposition, diffusion and aggregation model.

The Finite-Size Scaling Study of the Specific Heat and the Binder Parameter of the Two-Dimensional Ising Model for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

Approximate closed form expressions are developed for generalized elliptic type integrals using binomial coefficients. There are utilized to obtain closed form expressions for the Epstein-Hubbell (EH) generalized elliptic-type integral. Numerical test results are also reported. The convergence of series is tested by the concrete cases for values parameters. The formulae obtained are valid for arbitrary parameters values.

Hidrojen depolama malzemeleri için MgH2'nin yapısal ve elektronik özellikleri

The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4u2009≤u2009Lu2009≤u20098. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of Tc(∞)u2009=u20096.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent...