ANTIFERROMAGNETIC ISING MODEL DECORATED WITH D-VECTOR SPINS: TRANSVERSAL AND LONGITUDINAL LOCAL FIELDS EFFECTS

1995 ◽  
Vol 09 (26) ◽  
pp. 3387-3400 ◽  
Author(s):  
R. J. VASCONCELOS DOS SANTOS ◽  
S. COUTINHO
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Local Field ◽  
Local Fields ◽  
Square Lattice ◽  
Antiferromagnetic Ising Model

The effect of a local field acting on decorating classical D-vector bond spins of an antiferromagnetic Ising model on the square lattice is studied for both the annealed isotropic and the axial decorated cases. In both models the effect on the phase diagrams of the transversal and the longitudinal components of the local field acting on the decorating spins are fully analyzed and discussed.

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.

Phase Diagrams of Diluted Mixed Spin Ising Model on Square Lattice

1998 ◽  
Vol 210 (1) ◽  
pp. 229-235 ◽  
Author(s):  
Z.H. Xin ◽  
G.Z. Wei ◽  
G.Z. Wei ◽  
T.S. Liu ◽  
T.S. Liu
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Square Lattice ◽  
Mixed Spin

Thermodynamic quantities and phase diagrams of spin-1 Blume–Capel bilayer Ising model

2015 ◽  
Vol 29 (20) ◽  
pp. 1550141 ◽  
Author(s):  
Ersin Kantar ◽  
Mehmet Ertaş
Keyword(s):  
Field Theory ◽  
Ising Model ◽  
Phase Diagrams ◽  
Effective Field Theory ◽  
Critical Behavior ◽  
Tricritical Point ◽  
Effective Field ◽  
Square Lattice ◽  
Thermodynamic Quantities ◽  
Hamiltonian Parameters

An effective field theory with correlations has been used to study the critical behavior of the spin-1 Blume–Capel bilayer Ising model on a square lattice. The effects of the Hamiltonian parameters on thermodynamic quantities and phase diagrams are investigated in detail. We found that the system exhibits the first and the second order transitions as well as tricritical point. Furthermore, we have observed that the change of tricritical point values depends on interaction parameters.

Phase Diagrams of a 2D Dilute Antiferromagnetic Ising Model with Charged Impurities

2018 ◽  
Vol 32 (6) ◽  
pp. 1831-1835 ◽  
Author(s):  
Yu. D. Panov ◽  
K. S. Budrin ◽  
V. A. Ulitko ◽  
A. A. Chikov ◽  
A. S. Moskvin
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Antiferromagnetic Ising Model

scholarly journals Phase transitions of antiferromagnetic Ising spins on the zigzag surface of an asymmetrical Husimi lattice

2019 ◽  
Vol 6 (3) ◽  
pp. 181500 ◽  
Author(s):  
Ran Huang ◽  
Purushottam D. Gujrati
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Spontaneous Magnetization ◽  
Square Lattice ◽  
Two Dimensional ◽  
Simple Formulation ◽  
First Order ◽  
Husimi Lattice ◽  
Antiferromagnetic Ising Model ◽  
Ising Spins

An asymmetrical two-dimensional Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice, which we have previously applied to study polymers near a surface. The model retains the advantages of simple formulation and exact calculation of the conventional Bethe-like lattices. An antiferromagnetic Ising model is solved on the surface of this lattice to evaluate thermal properties such as free energy, energy density and entropy, from which we have successfully identified a first-order order–disorder transition other than the spontaneous magnetization, and a secondary transition on the supercooled state indicated by the Kauzmann paradox.

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