THE SIMULATION OF THE TWO-DIMENSIONAL ISING MODEL IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD ON THE CREUTZ CELLULAR AUTOMATON

2000 ◽  
Vol 11 (03) ◽  
pp. 561-572 ◽  
Author(s):  
B. KUTLU ◽  
M. KASAP ◽  
S. TURAN
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The two-dimensional Ising model in a small external magnetic field, is simulated on the Creutz cellular automaton. The values of the static critical exponents for 0.0025 ≤ h ≤ 0.025 are estimated within the framework of the finite size scaling theory. The value of the field critical exponent is in a good agreement with its theoretical value of δ = 15. The results for 0.0025 ≤ h ≤ 0.025 are compatible with Ising critical behavior for T < Tc.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

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

2010 ◽  
Vol 65 (8-9) ◽  
pp. 705-710 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Cellular Automaton ◽  
Finite Size ◽  
Fractal Dimensions ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Linear Dimensions ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for the lattice with L = 80, 120, and 160. The values of the fractal dimensions are compared with the results of former studies. As increasing the linear dimensions they are in good agreement with those. The fractals obtained by using the model of DLA are simulated on the Creutz cellular automaton by using a two-bit demon. The values computed for the critical temperature and the static critical exponents within the framework of the finite-size scaling theory are in agreement with the results of other simulations and theoretical values

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.

THE SIMULATION OF THE 2D FERROMAGNETIC BLUME–CAPEL MODEL ON A CELLULAR AUTOMATON

2001 ◽  
Vol 12 (09) ◽  
pp. 1401-1413 ◽  
Author(s):  
B. KUTLU
Keyword(s):  
Critical Temperature ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Finite Size ◽  
Scaling Theory ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton

The two-dimensional ferromagnetic Blume–Capel model is simulated on a cellular automaton, which based on the Creutz cellular automaton for square lattice. The values of the critical temperature and the static critical exponents are estimated within the framework of the finite-size scaling theory for 0 ≤ D/J ≤ 1.5. The results are compatible with the universal Ising critical behavior.

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.

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