Critical Properties of Two-dimensional Anisotropic Ising Model on a Square Lattice

2017 ◽  
Vol 30 (8) ◽  
pp. 2187-2195 ◽  
Author(s):  
D. Farsal ◽  
M. Snina ◽  
M. Badia ◽  
M. Bennai
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Two Dimensional ◽  
Critical Properties

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 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.

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.

Critical properties of a random transverse crystal field Ising model with bond dilution

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ling Wen ◽  
Yan Shi-Lei
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Effective Field ◽  
Square Lattice ◽  
Critical Properties ◽  
Strong Bond ◽  
Ordered Phases ◽  
Bond Dilution ◽  
Global Phase Diagrams

AbstractWithin effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.

Numerical evaluations of the critical properties of the two-dimensional Ising model

1975 ◽  
Vol 11 (1) ◽  
pp. 377-386 ◽  
Author(s):  
Leo P. Kadanoff ◽  
Anthony Houghton
Keyword(s):  
Ising Model ◽  
Two Dimensional ◽  
Critical Properties

Local three-spin correlations in the free-fermion and planar Ising models

1989 ◽  
Vol 423 (1865) ◽  
pp. 279-300 ◽  
Keyword(s):  
Ising Model ◽  
Ising Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Two Dimensional ◽  
Solvable Models ◽  
Spin Correlations ◽  
Fermion Model ◽  
Free Fermion Model

A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

Critical properties of an antiferromagnetic decorated Ising model on a square lattice

2020 ◽  
Vol 46 (10) ◽  
pp. 1016-1020
Author(s):  
V. A. Mutailamov ◽  
A. K. Murtazaev
Keyword(s):  
Ising Model ◽  
Square Lattice ◽  
Critical Properties
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