Critical Behavior of Spin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">S</mml:mi></mml:math>Antiferromagnetic Ising Model on Triangular Lattice

Lipowski, Adam; Horiguchi, T.; Lipowska, Dorota

doi:10.1103/physrevlett.74.3888

Cited by 26 publications

(41 citation statements)

References 7 publications

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“…The shape of this phase diagram has already been explained in Ref. [17]; here we note some additional interesting behaviors which can be predicted (following Ref. [3](b)) using the exponents associated with vortices.…”

Section: Finite Temperature Behaviorsupporting

confidence: 77%

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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Section: Finite Temperature Behaviorsupporting

confidence: 77%

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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“…A richer behavior is shown by the large-S triangular Ising antiferromagnet: the height field ensemble for the ground state is 'smooth' (i.e. the ground state has long-range order), and then as T is increased there are two transitions at finite T , first to a critical state and then to a disordered one (Lipowski et al , 1995). Since we find that the CPAFM model is 'smooth' at T = 0, it seems quite plausible that it undergoes analogous transitions at T > 0.…”

Section: Discussionmentioning

confidence: 99%

A constrained Potts antiferromagnet model with an interface representation

Burton

Henley

1997

J. Phys. A: Math. Gen.

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We define a four-state Potts model ensemble on the square lattice, with the constraints that neighboring spins must have different values, and that no plaquette may contain all four states. The spin configurations may be mapped into those of a 2-dimensional interface in a 2+5 dimensional space. If this interface is in a Gaussian rough phase (as is the case for most other models with such a mapping), then the spin correlations are critical and their exponents can be related to the stiffness governing the interface fluctuations. Results of our Monte Carlo simulations show height fluctuations with an anomalous dependence on wavevector, intermediate between the behaviors expected in a rough phase and in a smooth phase; we argue that the smooth phase (which would imply long-range spin order) is the best interpretation.

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“…In this model, the ground state configuration is solved exactly [3]. The critical behaviour of spin S antiferromagnetic Ising model on a triangular lattice was investigated by Lipowski et al [4]. They have shown that the ground state of such a model maps to a certain solid-on-solid (SOS) model.…”

Section: Introductionmentioning

confidence: 97%

Dynamics of Ising spins with antiferromagnetic bonds on a triangular lattice

Ismail¹,

Salem

2003

Physica Status Solidi (b)

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Six-coupled Ising spins on a triangular lattice with antiferromagnetic (AF) nearest neighbour and ferromagnetic (F) next-nearest neighbour interactions are investigated by Glauber dynamics. The system is fully frustrated and has seven non-trivial local energy minima in both clusters. The ground state has four degenerate states with energy -6. These states are separated by the energy barrier ∆E = 4.0 to invert spins in the ground state. The dynamics of AF-F and F-AF coupling clusters are solved exactly. Each cluster contributes as many long relaxation times as it has non-trivial local energy minima. The barriers against inversion of the clusters take only two values, 0 and 4|J|. In the paramagnetic case (PM), there is no diverging relaxation time. In the ferromagnetic case (FM), there is only one long-lived mode. The longest relaxation times follow an Arrhenius law. Both AF-F and F-AF clusters undergo a zero-temperature phase transition. The real and imaginary parts of the dynamic susceptibility display maxima if plotted versus temperature. The frequency dependence of the susceptibilities explain the effect of frustration. The real part reveals two plateaus and the imaginary part displays two corresponding maxima if they are plotted as functions of the logarithm of frequency. The Argand plots show two overlapping semicircles for fixed frequency at low temperature, indicating the time separation of the modes.

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Critical Behavior of SpinSAntiferromagnetic Ising Model on Triangular Lattice

Cited by 26 publications

References 7 publications

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

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

A constrained Potts antiferromagnet model with an interface representation

Dynamics of Ising spins with antiferromagnetic bonds on a triangular lattice

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