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    The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton
    (Springer/Plenum Publishers, 2012) Merdan, Z.; Guzelsoy, E.
    The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4a parts per thousand currency signLa parts per thousand currency sign8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be beta=0.49(7), beta=0.49(5), beta=0.50(1) and gamma=1.04(4), gamma=1.03(4), gamma=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of beta=0.5 and gamma=1. The values for the critical temperature of the infinite lattice T (c) (a)=6.6788(65), T (c) (a)=6.6798(69), T (c) (a)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4a parts per thousand currency signLa parts per thousand currency sign8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T (c) (a)=6.6817(15), T (c) (a)=6.6802(2), the dynamic Monte Carlo result of T (c) (a)=6.6803(1), the cluster Monte Carlo result of T (c) (a)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T (c) (a)=6.6802632 +/- 5x10(-5).
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    Öğe
    Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons
    (Amer Inst Physics, 2011) Merdan, Z.; Guzelsoy, E.
    The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 <= L <= 8. 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 T-c(infinity) = 6.6965(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 simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of T-c(infinity), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value T-c(infinity) = 6.6803(1), the cluster Monte Carlo value T-c(infinity) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm T-c(infinity) = 6.680263265+/-5 . 10(-5). The average values calculated for the critical exponent of the specific heat are a = -0.0402(15), -0.0393(12), -0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, alpha = -0.0391(11), agrees with the series expansions result, alpha = -0.12+/-0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, a >= 0+/-0.04. However, alpha=-0.0391(11) is inconsistent with the renormalization group prediction of alpha=0. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3610180]
  • Küçük Resim
    Öğe
    Finite-size scaling relations of the four-dimensional Ising model on the Creutz cellular automaton
    (2011) Merdan, Z.; Güzelsoy, E.
    The four-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 ? L ? 8. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for the 7, 14, and 21 independent simulations. The approximate values for the critical temperature of the infinite lattice, Tc(?) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without logarithmic factor), 6.6921(22) (without logarithmic factor), 6.6909(2) (without logarithmic factor), 6.6822(13) (with logarithmic factor), 6.6819(11) (with logarithmic factor), 6.6808(8) (with logarithmic factor) are obtained from the intersection points of specific heat curves, the Binder parameter curves and the straight line fit of specific heat maxima for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results, 6.6802(1) and 6.6808(8), are in very good agreement with the series expansion results of Tc(?) = 6.6817(15), 6.6802(2), the dynamic Monte Carlo result of Tc(?) = 6.6803(1), the cluster Monte Carlo result of Tc(?) = 6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm of Tc(?) = 6.6802632 ± 5-10-5 The average values obtained for the critical exponent of the specific heat are calculated as ? =-0.0402(15),-0.0393(12),-0.0391(11) for the 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained result, ? =-0.0391(11), is agreement with the series expansions results of ? =-0.12 ± 0.03 and the Monte Carlo using Metropolis and Wolff-cluster algorithm of a > 0+0.04. However, ? =-0.0391(11) isn't consistent with the renormalization group prediction of ? = 0. © Z. Merdan and E. Güzelsoy, 2011.