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

2005 ◽  
Vol 167 (1) ◽  
pp. 212-224 ◽  
Author(s):  
Z. Merdan ◽  
M. Bayırlı
Keyword(s):  
Ising Model ◽  
Cellular Automaton ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Linear Dimensions ◽  
Creutz Cellular Automaton

A FINITE-SIZE SCALING STUDY OF THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (05) ◽  
pp. 875-881 ◽  
Author(s):  
N. AKTEKIN ◽  
A. GÜNEN ◽  
Z. SAĞLAM
Keyword(s):  
Magnetic Susceptibility ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Size Scaling ◽  
Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton with increased precision. The data are analyzed according to the finite-size scaling relations available. The precision of the critical values related to magnetic susceptibility is improved by one digit, but in order to reach to the same precision for those related to the specific heat more simulation runs at the critical temperatures of the finite-size lattices are required.

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

2008 ◽  
Vol 22 (13) ◽  
pp. 1329-1341 ◽  
Author(s):  
G. MÜLAZIMOGLU ◽  
A. DURAN ◽  
Z. MERDAN ◽  
A. GUNEN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Finite Lattice ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
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 [Formula: see text] and [Formula: see text], which are also consistent with the precise results.

THE TEST OF THE FINITE-SIZE SCALING RELATIONS FOR THE FIVE-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (07) ◽  
pp. 1237-1245 ◽  
Author(s):  
N. AKTEKIN ◽  
Ş. ERKOÇ ◽  
M. KALAY
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The five-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4≤L≤16. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.52(7) and 1.25(11) using 6≤L≤12, respectively, which are in very good agreement with the Monte Carlo results and with the theoretical predictions of 5/2 and 5/4. The critical temperature for the infinite lattice is found to be 8.779(8) using 8≤L≤16 which is also in very good agreement with the recent precise results.

EFFECT OF THE NUMBER OF ENERGY LEVELS OF A DEMON FOR THE SIMULATION OF THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

2005 ◽  
Vol 16 (08) ◽  
pp. 1269-1278 ◽  
Author(s):  
Z. MERDAN ◽  
A. GUNEN ◽  
G. MULAZIMOGLU
Keyword(s):  
Magnetic Susceptibility ◽  
Ising Model ◽  
Cellular Automaton ◽  
Order Parameter ◽  
Energy Levels ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Binder Cumulant

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 FINITE-SIZE SCALING STUDY OF THE SPECIFIC HEAT AND THE BINDER PARAMETER FOR THE 7-DIMENSIONAL ISING MODEL

2007 ◽  
Vol 21 (04) ◽  
pp. 215-224 ◽  
Author(s):  
Z. MERDAN ◽  
D. ATILLE
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton ◽  
Binder Parameter

The 7-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 4, 6, 8. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T c = 12.866(2), T c = 12.871(2) and T c = 12.871(49) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise values of the Creutz cellular automaton results of T c = 12.8700(42), the 1/d-expansion result of T c = 12.8712, the series expansion result of T c = 12.86902(33), the dynamic Monte Carlo result of T c = 12.8667(50). The values obtained for the critical exponent of the specific heat, i.e., α = 0.011(76), α = -0.002, α = 0.011(5) and α = 0.082(32) corresponding to the above T c values, respectively, are in agreement with α = 0 predicted by the theory. Moreover the values for the Binder parameter are calculated as gL(T c ) = -1.022(28), gL(T c ) = -1.09, gL(T c ) = -1.01(12) and gL(T c ) = -1.34(55) corresponding to the above T c values, respectively.

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