scholarly journals CRITICAL DYNAMICS OF TWO-REPLICA CLUSTER ALGORITHMS

2001 ◽  
Vol 12 (02) ◽  
pp. 257-271
Author(s):  
X.-N. LI ◽  
J. MACHTA
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Cluster Algorithm ◽  
The Other ◽  
Square Lattice ◽  
Critical Dynamics ◽  
Two Dimensional ◽  
Cluster Algorithms ◽  
Dynamic Exponent

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

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.

Nonequilibrium critical dynamics of two dimensional Ising model under slow cooling and heating

2021 ◽  
Vol 71 (2) ◽  
pp. 200-209
Author(s):  
Kangeun JEONG* ◽  
Bongsoo KIM ◽  
Sung Jong LEE
Keyword(s):  
Ising Model ◽  
Critical Dynamics ◽  
Two Dimensional ◽  
Slow Cooling

scholarly journals CLUSTER VS. SINGLE-SPIN ALGORITHMS—WHICH ARE MORE EFFICIENT?

1994 ◽  
Vol 05 (01) ◽  
pp. 1-14 ◽  
Author(s):  
N. ITO ◽  
G.A. KOHRING
Keyword(s):  
Ising Model ◽  
Critical Exponents ◽  
Cluster Algorithm ◽  
Computer Time ◽  
System Size ◽  
Statistical Accuracy ◽  
Single Spin ◽  
Cluster Algorithms ◽  
Vector Computers ◽  
Single Cluster

A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms of site updates per second or the dynamical critical exponents. Our main result is that the cluster algorithms become more efficient when the system size, Ld, exceeds, L~70–300 for d=2 and l~80–200 for d=3. The exact value of the crossover is dependent upon the computer being used. The lower end of the crossover range is typical of workstations while the higher end is typical of vector computers. Hence, even for workstations, the system sizes needed for efficient use of the cluster algorithm is relatively large.

A CORRELATION BETWEEN PERCOLATION MODEL AND ISING MODEL

1996 ◽  
Vol 07 (04) ◽  
pp. 609-612 ◽  
Author(s):  
R. HACKL ◽  
I. MORGENSTERN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Percolation Threshold ◽  
Higher Dimensions ◽  
Percolation Model ◽  
Critical Values ◽  
Square Lattice ◽  
Approximation Formula ◽  
Two Dimensional

In this article we will expose a connection between critical values of percolation and Ising model, i.e., the percolation threshold pc, and the critical temperature Tc and energy Ec, respectively, by the approximation [Formula: see text]. For the two-dimensional square lattice even the identity holds. For higher dimensions — up to d = 7 — and other lattice types we find remarkably small differences from one to five percent.

Effects of Superaging and Percolation Crossover on the Nonequilibrium Critical Behavior of the Two-Dimensional Disordered Ising Model

JETP Letters ◽  
2018 ◽  
Vol 107 (9) ◽  
pp. 569-576 ◽  
Author(s):  
V. V. Prudnikov ◽  
P. V. Prudnikov ◽  
E. A. Pospelov ◽  
P. N. Malyarenko
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Two Dimensional
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