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1
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On Gibbs Measures of the Potts Model with Three Competing Interactions on Cayley Tree of Order 3

100%
Akin H., Saygılı H.
Acta Physica Polonica A
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2016
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vol. 129
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issue 4
845-848
EN
In this paper, we consider the Potts model with competing interactions on the Cayley tree of order three. We give the Potts model on the Cayley tree and its recursion relation. We construct the Gibbs states corresponding to the model by using Markov random field method. We calculate the critical curve, such that there is a phase transition for the model. We show that there are phase transition of the model for some given parameters. We extend the results obtained by Akin and Temir (Condensed Matt. Phys. 14, 23003 (2011)).
2
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Effect of On-Site Coulomb Repulsion on Phase Transitions in Exactly Solved Spin-Electron Model

100%
Gálisová L., Strečka J., Tanaka A., Verkholyak T.
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issue 5
942-943
EN
A hybrid lattice-statistical model on doubly decorated planar lattices, which have localized Ising spins at their nodal lattice sites and two itinerant electrons at each pair of decorating sites, is exactly solved by the use of a generalized decoration-iteration transformation. Our main attention is focused on an influence of the on-site Coulomb repulsion on ground-state properties and critical behavior of the investigated system.
3
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Magnetization and Susceptibility of a Diluted Triangular Ising Antiferromagnet in a Field

100%
Borovský M., Žukovič M., Bobák A.
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vol. 126
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issue 1
16-17
EN
Within the framework of the effective-field theory with correlations we investigate effects of an external magnetic field and random site dilution on basic thermodynamic quantities, such as the magnetization and the magnetic susceptibility, on the geometrically frustrated triangular lattice Ising antiferromagnet. Behavior of these quantities is presented in the temperature-field parameter space for selected mild degrees of dilution. It is found that, besides the anomalies associated with phase transitions from the ferrimagnetic to the paramagnetic state, in certain regions of the parameter space these functions display some more anomalies and peculiarities, as a result of joint effects of the geometrical frustration, magnetic dilution, thermal fluctuations and the applied magnetic field.
4
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Description of Extreme Gibbs Measures for the Ising Model with Three Interactions

100%
Akin H., Ganikhodjaev N., Temir S., Uguz S.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
484-487
EN
In this paper, we consider an Ising model with three competing interactions (nearest neighbor, next-nearest neighbor, and ternary prolonged neighbor) on the Cayley tree of order two, investigated by Ganikhodjaev et al. We study translation-invariant Gibbs measures of the Ising model with these competing interactions. Also, we investigate the set of the extreme Gibbs measures called Markov random fields with memory 2 of the model.
5
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Ground-State Properties of the Spin-1/2 Heisenberg-Ising Bond Alternating Chain with Dzyaloshinskii-Moriya Interaction

100%
Strečka J., Gálisová L., Derzhko O.
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issue 5
742-744
EN
Ground-state energy is exactly calculated for the spin-1/2 Heisenberg-Ising bond alternating chain with the Dzyaloshinskii-Moriya interaction. Under certain condition, which relates a strength of the Ising, Heisenberg and Dzyaloshinskii-Moriya interactions, the ground-state energy exhibits an interesting nonanalytic behavior accompanied with a gapless excitation spectrum.
6
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The Competing Interactions on a Cayley Tree-Like Lattice: Pentagonal Chandelier

100%
Uguz S., Ganikhodjaev N., Akin H., Temir S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1
114-118
EN
Different types of lattice spin systems with competing interactions have rich and interesting phase diagrams. In this study we present some new results for such systems involving the Ising spin system (i.e. σ = ± 1) using a generalization of the Cayley tree-like lattice approximation. We study the phase diagrams for the Ising model on a Cayley tree-like lattice, a new lattice type called pentagonal chandelier, with competing nearest-neighbor interactions J_1, prolonged next-nearest-neighbor interactions J_{p} and one-level next-nearest-neighbor senary interactions J_{l_1}^{(6)}. The colored phase diagrams contain some multicritical Lifshitz points that are at nonzero temperature and many modulated new phases. We also investigate the variation of the wave vector with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of the system.
7
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Order-Disorder Transition in 2D Conserved Spin System with Cooperative Dynamics

100%
Hałagan K., Polanowski P.
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EN
In this work Monte Carlo simulations with usage of dynamic lattice liquid model are presented, instead of the widely used direct exchange or vacancy dynamics, to investigate the dynamics of phase separation phenomenon in spin conserved system with all lattice sites occupied. The dynamic behaviour of domain growth and particle diffusion is discussed for the modified conserved order parameter Ising model. The dynamic lattice liquid model dynamics enables non-locally correlated relaxation dynamics and allows to simulate dense systems in absence of vacancies and parallel treatment of all spins. This approach involves cooperative movement of system elements enabling observation of the order-disorder phase transition in a system with highly correlated motions. Simulations were performed on 2D triangular lattice for several investigated temperatures. Presented results include temporal evolution of domain morphology and diffusion of system elements.
8
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Low-Temperature Properties of Ising Antiferromagnet on a Stacked Triangular Lattice

100%
Žukovič M., Mižišin L., Bobák A.
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vol. 126
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issue 1
40-41
EN
An Ising antiferromagnet on a stacked triangular lattice in zero field is studied by Monte Carlo simulations, focusing on the character of the low-temperature phase and the effect of the relative strength of the exchange interaction in the stacking direction α. Our results support the presence of the 3D Wannier phase, with the sublattice magnetization structure (m, -m, 0) and power-law decaying m with the lattice size. The extent of this low-temperature phase shrinks with decreasing α, however, it appears even at very low values if it is accessed from higher temperatures by sufficiently slow cooling.
9
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Behaviors of Phase Diagrams of Ising Model with Competing Ternary and Binary Interactions on a Cayley Tree of Arbitrary Order

100%
Akin H., Ganikhodjaev N., Uguz S., Temir S.
Acta Physica Polonica A
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2012
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vol. 121
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issue 1
104-107
EN
An Ising model with competing interactions has recently been studied extensively because of the appearance of nontrivial magnetic orderings. In this paper, we study the phase diagrams for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{t_{p}} on a Cayley tree of arbitrary order k and compare with the phase diagrams obtained in Uguz et al. and Vannimenus results for the Ising model on a Cayley tree with competing nearest-neighbor interactions J and ternary prolonged interactions J_{p}. For some values of k, we obtain phase diagrams of the model. We clarify the role of order k of the Cayley tree. We also plot the variation of the wave vector with temperature.
10
Content available remote

Monte Carlo Study of a Spin-3/2 Blume-Emery-Griffiths Model on a Honeycomb Lattice

88%
Žukovič M., Jaščur M.
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vol. 126
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issue 1
36-37
EN
We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with correlations. The locations of the order-disorder phase boundaries are estimated from thermal variations of the magnetic susceptibility curves. It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations. However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.
11
Content available remote

Ordering in Triangular Lattice Ising Antiferromagnet Due to Dilution and Magnetic Field

75%
Žukovič M., Borovský M., Bobák A.
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issue 5
740-741
EN
We study effects of an external magnetic field and random site dilution on the magnetic ordering in the geometrically frustrated triangular lattice Ising antiferromagnet by the use of an effective-field theory with correlations. In particular, we find that already a small amount of the quenched dilution locally relieves the frustration which in the presence of the external field is manifested by multiple splitting of a broad frustration-induced 1/3 magnetization plateau. Depending on the field strength, the dilution can either decrease or increase the magnetization or even change its effect from decreasing to increasing.
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