Computation of critical exponents for two-dimensional ising model on a cellular automaton

1994 ◽  
Vol 75 (3-4) ◽  
pp. 757-763 ◽  
Author(s):  
B. Kutlu ◽  
N. Aktekin
Keyword(s):  
Ising Model ◽  
Cellular Automaton ◽  
Critical Exponents ◽  
Two Dimensional

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.

A Test of Scaling Theory on the Critical Isotherm

1972 ◽  
Vol 50 (24) ◽  
pp. 3117-3122 ◽  
Author(s):  
D. D. Betts ◽  
L. Filipow
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Excellent Agreement ◽  
Critical Behavior ◽  
Critical Exponents ◽  
High Field ◽  
Two Dimensional ◽  
Amplitude Ratios ◽  
Critical Amplitude ◽  
Critical Isotherm

Using recently extended data of Sykes et al. on the high field expansion of the free energy of the two-dimensional spin-1/2 Ising model the critical behavior of the magnetization and its first six temperature derivatives are examined on the critical isotherm. The estimates of the critical exponents and the critical amplitude ratios are found to be in reasonable to excellent agreement with scaling theories.

ISING MODELS ON TWO-DIMENSIONAL QUASI-CRYSTALS: SOME EXACT RESULTS

1988 ◽  
Vol 02 (01) ◽  
pp. 49-63 ◽  
Author(s):  
T. C. CHOY
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Ising Models ◽  
Critical Surface ◽  
Exact Results ◽  
Two Dimensional ◽  
Soluble Model ◽  
De Bruijn ◽  
Quasi Crystals ◽  
Conventional Picture

Exactly soluble Z-invariant (or Baxter) models of statistical mechanics are generalised on two-dimensional Penrose lattices based on the de Bruijn construction. A unique soluble model is obtained for each realization of the Penrose lattice. Analysis of these models shows that they are soluble along a line in parameter space which intersects the critical surface at a point that can be determined exactly. In the Ising case, critical exponents along this line are identical with the regular two-dimensional Ising model thus supporting the conventional picture of the universality hypothesis.

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.

scholarly journals SHORT-TIME DYNAMIC EXPONENTS OF AN ISING MODEL WITH COMPETING INTERACTIONS

2003 ◽  
Vol 17 (05n06) ◽  
pp. 209-218 ◽  
Author(s):  
NELSON ALVES ◽  
JOSÉ ROBERTO DRUGOWICH DE FELÍCIO
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Order Parameter ◽  
Nearest Neighbor ◽  
Time Correlation ◽  
Time Behavior ◽  
Two Dimensional ◽  
Competing Interactions ◽  
Time Dynamic ◽  
Short Time

In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.

Sign in / Sign up

Export Citation Format

Share Document