Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

Harold J.W. Zandvliet

doi:10.1080/01411594.2022.2162897

Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

Harold J.W. Zandvliet^*

^*Corresponding author for this work

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Abstract

We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor ((Formula presented.)) and isotropic next-nearest neighbor ((Formula presented.)) interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when (Formula presented.) if (Formula presented.) and (Formula presented.) have the same sign or (Formula presented.) if (Formula presented.) and (Formula presented.) have opposite signs.

Original language	English
Journal	Phase transitions
Early online date	12 Jan 2023
DOIs	https://doi.org/10.1080/01411594.2022.2162897
Publication status	E-pub ahead of print/First online - 12 Jan 2023

Keywords

domain wall free energy
Ising
order–disorder phase transition
Phase diagram
UT-Hybrid-D

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10.1080/01411594.2022.2162897Licence: CC BY-NC-ND

Phase diagram of the square 2D Ising lattice with nearest neighbor and next nearest neighbor interactions (1)Final published version, 1.31 MBLicence: CC BY-NC-ND

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title = "Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions",

abstract = "We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor ((Formula presented.)) and isotropic next-nearest neighbor ((Formula presented.)) interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when (Formula presented.) if (Formula presented.) and (Formula presented.) have the same sign or (Formula presented.) if (Formula presented.) and (Formula presented.) have opposite signs.",

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doi = "10.1080/01411594.2022.2162897",

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T1 - Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

AU - Zandvliet, Harold J.W.

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Y1 - 2023/1/12

N2 - We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor ((Formula presented.)) and isotropic next-nearest neighbor ((Formula presented.)) interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when (Formula presented.) if (Formula presented.) and (Formula presented.) have the same sign or (Formula presented.) if (Formula presented.) and (Formula presented.) have opposite signs.

AB - We have determined the temperature dependent phase diagram of the square 2D Ising lattice with anisotropic nearest neighbor ((Formula presented.)) and isotropic next-nearest neighbor ((Formula presented.)) interactions. The phase boundaries between the various ordered phases (ferromagnetic, antiferromagnetic and striped antiferromagnetic) and the disordered phase (paramagnetic) are obtained by considering the domain wall free energy. Although the phase boundary equations are not exact, they provide a very accurate description when the nearest neighbor interactions are stronger than the next-nearest neighbor interaction. The square 2D Ising lattice does not exhibit a phase transition when (Formula presented.) if (Formula presented.) and (Formula presented.) have the same sign or (Formula presented.) if (Formula presented.) and (Formula presented.) have opposite signs.

KW - domain wall free energy

KW - Ising

KW - order–disorder phase transition

KW - Phase diagram

KW - UT-Hybrid-D

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JO - Phase transitions

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SN - 0141-1594

ER -

Phase diagram of the square 2D Ising lattice with nearest neighbor and next-nearest neighbor interactions

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