Critical properties of an antiferromagnetic Ising model on a square lattice with interactions of the next-to-nearest neighbors

2011 ◽  
Vol 37 (12) ◽  
pp. 1001-1005 ◽  
Author(s):  
A. K. Murtazaev ◽  
M. K. Ramazanov ◽  
M. K. Badiev
Keyword(s):  
Ising Model ◽  
Nearest Neighbors ◽  
Square Lattice ◽  
Critical Properties ◽  
Antiferromagnetic Ising Model

Ising Antiferromagnet with Nearest-Neighbor and Next-Nearest-Neighbor Interactions on a Square Lattice

2014 ◽  
Vol 215 ◽  
pp. 17-21
Author(s):  
Akai K. Murtazaev ◽  
Magomedsheikh K. Ramazanov ◽  
Magomedzagir K. Badiev
Keyword(s):  
Nearest Neighbor ◽  
Finite Size ◽  
Nearest Neighbors ◽  
Correlation Radius ◽  
Square Lattice ◽  
Two Dimensional ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Ising Antiferromagnet ◽  
Antiferromagnetic Ising Model

The critical properties of two-dimensional antiferromagnetic Ising model in square lattice are investigated using the replica Monte-Carlo method with account of interactions of second nearest neighbors. The diagram of critical temperature dependence on an interaction value of second nearest neighbors is plotted. Static critical exponents of the heat capacity α, susceptibility γ, magnetization β, and correlation radius ν are calculated for this model using the finite-size scaling theory.

scholarly journals Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Finite Lattices ◽  
Antiferromagnetic Ising Model ◽  
Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

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.

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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