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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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2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

81%
Uguz S., Siap I., Akin H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
480-483
EN
In this paper, we study 2-dimensional finite cellular automata defined by hexagonal local rule with periodic boundary over the field Z_3. We construct the rule matrix corresponding to the hexagonal cellular automata. For some given coefficients and the number of columns of hexagonal information matrix, we prove that the hexagonal cellular automata are reversible.
3
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Description of Extreme Gibbs Measures for the Ising Model with Three Interactions

81%
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.
4
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Behavior of the Phase Diagrams of Potts Model οn Cayley Tree for Order Three

81%
Temir S., Ganikhodjaev N., Uguz S., Akin H.
Acta Physica Polonica A
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2013
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vol. 123
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issue 2
476-479
EN
The aim of this paper is to extend the results of Ganikhodjaev et al. to the three state Potts model with competing nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions on a Cayley tree for order 3 and compare with the phase diagrams obtained in Temir et al. and to study modulated phases arising from the frustration effects introduced by nearest-neighbor, prolonged next-nearest-neighbor and two-level triple neighbor interactions.
5
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Characterization of 2D Hybrid Cellular Automata with Periodic Boundary

81%
Acar E., Uguz S., Akin H.
Acta Physica Polonica A
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2017
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vol. 131
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issue 3
432-436
EN
We investigate main theoretical aspects of two-dimensional linear-hybrid cellular automata with periodic boundary condition over the Galois field GF(2). We focus on the characterization of two-dimensional hybrid linear cellular automata by way of a special algorithm. Here we set up a relation between reversibility of cellular automata and characterization of two-dimensional hybrid linear cellular automata with a special boundary conditions, i.e. periodic case. The determination of the characterization problem of special type of cellular automaton is studied by means of the matrix algebra theory. It is believed that this type of cellular automata could find many different applications in special case situations, e.g. image processing area, textile design, video processing, DNA research, etc., in the near future.
6
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2D Cellular Automata with an Image Processing Application

81%
Uguz S., Sahin U., Siap I., Akin H.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
435-438
EN
This paper investigates the theoretical aspects of two-dimensional linear cellular automata with image applications. We consider geometrical and visual aspects of patterns generated by cellular automata evolution. The present work focuses on the theory of two-dimensional linear cellular automata with respect to uniform periodic and adiabatic boundary cellular automata conditions. Multiple copies of any arbitrary image corresponding to cellular automata find so many applications in real life situation e.g. textile design, DNA genetics research, etc.
7
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The Competing Interactions on a Cayley Tree-Like Lattice: Pentagonal Chandelier

81%
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.
8
Content available remote

Existence of p-Adic Quasi Gibbs Measures for Mixed Type p-Adic Ising λ-Model

81%
Dogan M., Akin H., Mukhamedov F.
Acta Physica Polonica A
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2016
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vol. 129
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issue 4
861-864
EN
We consider nearest-neighbors and next nearest-neighbors p-adic Ising λ-model with spin values {∓ 1} on a Cayley tree of order two. First we prove that the model satisfies the Kolmogorov consistency condition and then we prove that the nonlinear equation corresponding to the model has at least two solutions in Q_{p}, where p is a prime number p ≥ 3. One of the roots is in ε_{p} and the others are in Q_{p}\ε_{p}. If the nonlinear equation has more than one non-trivial solutions for the model then we conclude that p-adic quasi Gibbs measure exists for the model.
9
Content available remote

On Pseudo Random Bit Generators via Two-Dimensional Hybrid Cellular Automata

81%
Temiz F., Siap I., Akin H.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
534-537
EN
In this work, we study the structure of two-dimensional linear hybrid cellular automata with respect to adiabatic boundary condition. Further, we check the performance of hybrid cellular automata constructed through the members of this family in generating pseudo random bits.
10
Content available remote

One-Dimensional Cellular Automata with Reflective Boundary Conditions and Radius Three

81%
Akin H., Siap I., Uguz S.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
405-407
EN
A family of one-dimensional finite linear cellular automata with reflective boundary condition over the field Z_p is defined. The generalizations are the radius and the field that states take values. Here, we establish a connection between reversibility of cellular automata and the rule matrix of the cellular automata with radius three. Also, we prove that the reverse CA of this family again falls into this family.
11
Content available remote

Behaviors of Phase Diagrams of Ising Model with Competing Ternary and Binary Interactions on a Cayley Tree of Arbitrary Order

81%
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.
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