Low-Temperature Behaviors of Antiferromagnetic Ising Model of Infinite-Spin on Triangular Lattice

Horiguchi, T.; Nagai, Ojiro; Miyashita, Seiji; Miyatake, Y.; Seo, Yoshiki

doi:10.1143/jpsj.61.3114

Cited by 9 publications

(4 citation statements)

References 15 publications

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“…The limit A → 1 corresponds to the isotropic Heisenberg model [6] whereas the limit A → ∞ corresponds to an infinite spin Ising model. [7] Southern and Xu [8] have previously studied the Heisenberg limit and found direct evidence for a vortex unbinding transition at finite temperature even though the spin stiffness vanishes on large length scales. This latter fact indicates that the spin correlations decay exponentially at all finite temperatures T .…”

Section: The Modelmentioning

confidence: 99%

“…Similar behaviour has been reported previously for other frustrated systems on the triangular lattice. The antiferromagnetic spin 1/2 Ising model with both nearest and next-nearest neighbour interactions [19,20] as well as the antiferromagnetic S = ∞ nearest neighbour model [7,21,22] exhibit this phenomena in the temperature range where a KT phase occurs. In our case, the switching is due to the wave-like variations in ψ which can produce "vortex-like" variations in the local magnetization vector M 0 .…”

Section: Microscopic Propertiesmentioning

confidence: 99%

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Monte Carlo study of the anisotropic Heisenberg antiferromagnet on the triangular lattice

Stephan

Southern

2000

Phys. Rev. B

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We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis exchange anisotropy on the triangular lattice. Both the free energy cost for long-wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus, respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented.

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Section: The Modelmentioning

confidence: 99%

Section: Microscopic Propertiesmentioning

confidence: 99%

Monte Carlo study of the anisotropic Heisenberg antiferromagnet on the triangular lattice

Stephan

Southern

2000

Phys. Rev. B

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“…The key is to replace the uncorrelated noise function ξ(x, t) of Eq. (30) with a new correlated noise function having |ξ(q, t)| 2 ∼ 1/|q| 2 . This might be implemented by first constructing a random function with such correlations, and then updating flippable spins with probabilities determined by that function, in such a fashion as to satisfy detailed balance.…”

Section: Possible Improved Algorithmsmentioning

confidence: 99%

Zero-temperature phase transitions of an antiferromagnetic Ising model of general spin on a triangular lattice

Zeng

Henley

1997

Phys. Rev. B

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We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective Gaussian free energy, which enables us to calculate the critical exponents of various operators in terms of the stiffness constant of the interface. Monte Carlo simulations for the ground-state ensemble utilizing this interfacial representation are performed to study both the dynamical and the static properties of the model. This method yields more accurate numerical results for the critical exponents. By varying the spin magnitude in the model, we find that the model exhibits three phases with a Kosterlitz-Thouless phase transition at 3 2 < SKT < 2 and a locking phase transition at 5 2 < SL ≤ 3. The phase diagram at finite temperatures is also discussed.

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“…One way to alleviate the effects of frustration and thus to induce order is by increasing multiplicity of the local degrees of freedom, which can be achieved by increasing the magnitude of the spin variable S. The effect of the spin magnitude on critical properties of IATL has attracted considerable attention and numerous results on this topic have been reported in a series of papers [5][6][7][8][9][10][11][12][13]. A phenomenological theory lead to a conclusion that in the limit of S → ∞ the ground state shows (partial) antiferromagnetic LRO with two sublattices fully ordered and the third one disordered.…”

Section: Introductionmentioning

confidence: 99%

Absence of long-range order in a general spin-S kagome lattice Ising antiferromagnet

Semjan

Žukovič

2020

Physics Letters A

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The possibility of the emergence of some kind of long-range ordering (LRO) due to the increase of multiplicity of the local degrees of freedom (spin value S) is studied in an Ising antiferromagnet on a kagome lattice (IAKL) by Monte Carlo simulation. In particular, the critical exponent of the spin correlation function, obtained from a finite-size scaling analysis, is evaluated for various values of S, including S = ∞, with the goal to determine whether there exists some threshold value of the spin S C above which the system would show true or quasi-LRO, similar to a related model on a triangular lattice (IATL). It is found that, unlike in the IATL case, the IAKL model remains disordered for any spin value and any finite temperature.

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Low-Temperature Behaviors of Antiferromagnetic Ising Model of Infinite-Spin on Triangular Lattice

Cited by 9 publications

References 15 publications

Monte Carlo study of the anisotropic Heisenberg antiferromagnet on the triangular lattice

Monte Carlo study of the anisotropic Heisenberg antiferromagnet on the triangular lattice

Zero-temperature phase transitions of an antiferromagnetic Ising model of general spin on a triangular lattice

Absence of long-range order in a general spin-S kagome lattice Ising antiferromagnet

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