Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics C

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

Bülent Kutlu

Published Dec 1, 2003• 15 citations
Publisher

Abstract

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.

DOI
10.1142/s0129183103005443

Related papers

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

A. SOLAK, Bülent Kutlu

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.

International Journal of Modern Physics C•Dec 1, 2004•7 citations

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

Bülent Kutlu, M. Kasap, S. TURAN

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.

International Journal of Modern Physics C•May 1, 2000•8 citations

The Study of the Three-Dimensional Spin-3/2 Ising Model on a Cellular Automaton

Nurgül Seferoğlu

The spin-3/2 Ising model on the simple cubic lattice with nearest-neighbour ferromagnetic bilinear interaction (J > 0) is simulated on a cellular automaton by using the cooling algorithm improved from the Creutz cellular automaton. The phase diagrams of the model are constructed in the (D/J, kT/J) and (K/J, kT/J) plane. Comparison of the results are made with those of other methods. The temperature dependence of the order parameters and associated fluctuations are calculated at various of the model parameters and the static critical exponents are estimated within the framework of the finite-size scaling. The results are compatible with the universal Ising critical behavior except for D/J =−3 and K/J =−2.3.

Communications in Computational Physics•Sep 4, 2009•3 citations

The Mixed Spin 3 - Spin 3/2 Ferrimagnetic Ising Model on Cellular Automaton

Aycan Özkan

The mixed spin 3- spin 3/2 Ising model has been simulated using cooling algorithm on cellular automaton (CA). The simulations have been made in the interval -6<=D<=6 for J=1 for the square lattices with periodic boundary conditions. The ground state phase diagram of the model has different type ferrimagnetic orderings. Through D/J=2 line, compensation points occurs at kT/J=0. The values of the critical exponents ( ν, α, β and γ) are estimated within the framework of the finite-size scaling theory and power law relations for selected D/J values (-2, 0, 1, 2 and 4). The estimated critical exponent values are in a good agreement with their universal values of the two dimensional Ising model.

arXiv:1304.7740•Apr 29, 2013•0 citations

A simulation of the mixed spin 3–spin 3/2 ferrimagnetic Ising model

Aycan Özkan

The mixed spin 3–spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals −4 ≤ DA/J ≤ 8 and −4 ≤ DB/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through DA/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected DA/J values (−2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α′ = 0, β = 0.125, β′ = 0.875 and γ = γ′ = 1.75).

Phase Transitions•Sep 11, 2015•16 citations

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

Gökçe Mülazımoğlu, A. Duran, Ziya Merdan +1 more

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.

Modern Physics Letters B•May 30, 2008•6 citations
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 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 spin-3/2 Ising model on the simple cubic lattice with nearest-neighbour ferromagnetic bilinear interaction (J > 0) is simulated on a cellular automaton by using the cooling algorithm improved from the Creutz cellular automaton. The phase diagrams of the model are constructed in the (D/J, kT/J) and (K/J, kT/J) plane. Comparison of the results are made with those of other methods. The temperature dependence of the order parameters and associated fluctuations are calculated at various of the model parameters and the static critical exponents are estimated within the framework of the finite-size scaling. The results are compatible with the universal Ising critical behavior except for D/J =−3 and K/J =−2.3.
The mixed spin 3- spin 3/2 Ising model has been simulated using cooling algorithm on cellular automaton (CA). The simulations have been made in the interval -6<=D<=6 for J=1 for the square lattices with periodic boundary conditions. The ground state phase diagram of the model has different type ferrimagnetic orderings. Through D/J=2 line, compensation points occurs at kT/J=0. The values of the critical exponents ( ν, α, β and γ) are estimated within the framework of the finite-size scaling theory and power law relations for selected D/J values (-2, 0, 1, 2 and 4). The estimated critical exponent values are in a good agreement with their universal values of the two dimensional Ising model.
The mixed spin 3–spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals −4 ≤ DA/J ≤ 8 and −4 ≤ DB/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through DA/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected DA/J values (−2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α′ = 0, β = 0.125, β′ = 0.875 and γ = γ′ = 1.75).
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.