Phase transitions in the antiferromagnetic ising model on a square lattice with next-nearest-neighbor interactions

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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Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

Phase Transitions ◽

10.1080/01411594.2018.1428975 ◽

2018 ◽

Vol 91 (6) ◽

pp. 610-618 ◽

Cited By ~ 8

Author(s):

M. K. Ramazanov ◽

A. K. Murtazaev ◽

M. A. Magomedov ◽

M. K. Badiev

Keyword(s):

Phase Transitions ◽

Ising Model ◽

Thermodynamic Properties ◽

Nearest Neighbor ◽

Kagome Lattice ◽

Kagomé Lattice ◽

Antiferromagnetic Ising Model

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Phase transitions and critical characteristics in the layered antiferromagnetic Ising model with next-nearest-neighbor intralayer interactions

JETP Letters ◽

10.1134/s0021364015100100 ◽

2015 ◽

Vol 101 (10) ◽

pp. 714-718 ◽

Cited By ~ 18

Author(s):

M. K. Ramazanov ◽

A. K. Murtazaev

Keyword(s):

Phase Transitions ◽

Ising Model ◽

Nearest Neighbor ◽

Critical Characteristics ◽

Antiferromagnetic Ising Model

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Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

Journal of Experimental and Theoretical Physics ◽

10.1134/s1063776115010057 ◽

2015 ◽

Vol 120 (1) ◽

pp. 110-114 ◽

Cited By ~ 25

Author(s):

A. K. Murtazaev ◽

M. K. Ramazanov ◽

F. A. Kassan-Ogly ◽

D. R. Kurbanova

Keyword(s):

Phase Transitions ◽

Ising Model ◽

Nearest Neighbors ◽

Body Centered Cubic ◽

Cubic Lattice ◽

Antiferromagnetic Ising Model ◽

Body Centered Cubic Lattice

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

SciPost Physics ◽

10.21468/scipostphys.8.3.032 ◽

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.

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