Ahmet Nihat Berker

Berker, Ahmet Nihat

Name Variants

Nihat Berker A.
BERKER, Ahmet Nihat
Ahmet Nihat, Berker
Berker,Ahmet Nihat
Berker, AHMET NIHAT
A. Berker
B.,Ahmet Nihat
Berker,A.N.
Berker, A.
Berker, Ahmet Nihat
Berker N.
Ahmet Nihat Berker
Ahmet Nihat BERKER
Berker, A. N.
B., Ahmet Nihat
AHMET NIHAT BERKER
A. N. Berker
BERKER, AHMET NIHAT
Berker A.
Berker, A. Nihat

Job Title

Prof. Dr.

Email Address

nihatberker@khas.edu.tr

ORCID ID

0000-0002-5172-2172

Scopus Author ID

6701401118

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Scholarly Output

27

Articles

27

Citation Count

0

Supervised Theses

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Now showing 1 - 10 of 27

Axial, planar-diagonal, body-diagonal fields on the cubic-spin spin glass in d=3: A plethora of ordered phases under finite fields
(Amer Physical Soc, 2024) Berker, Ahmet Nihat; Sarman, Deniz; Berker, A. Nihat
A nematic phase, previously seen in the d = 3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the hightemperature disordered phase, for number of spin components n >= 3, in spatial dimension d = 3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), qualitatively different from the conventional spin-glass phase diagram topology, are seen. The chaotic rescaling behaviors and their Lyapunov exponents are calculated in each of these spin-glass phase diagram topologies. These results are obtained from renormalization-group calculations that are exact on the d = 3 hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. Axial, planar-diagonal, or body-diagonal finite-strength uniform fields are applied to n = 2 and 3 component cubic-spin spin-glass systems in d=3.
Driven and Non-Driven Surface Chaos in Spin-Glass Sponges
(Pergamon-elsevier Science Ltd, 2023) Pektas, Yigit Ertac; Berker, Ahmet Nihat; Artun, E. Can; Berker, A. Nihat
A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d = 3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated. The smooth surface does not have spin-glass ordering in the absence of bulk spin-glass ordering and always has spin-glass ordering when the bulk is spin-glass ordered. With fractal (d > 2) surfaces, a sponge is obtained and has surface spin-glass ordering also in the absence of bulk spin-glass ordering. The phase diagram has the only-surface-spin-glass ordered phase, the bulk and surface spin-glass ordered phase, and the disordered phase, and a special multicritical point where these three phases meet. All spin-glass phases have distinct chaotic renormalization-group trajectories, with distinct Lyapunov and runaway exponents which we have calculated.
Global Ashkin-Teller Phase Diagrams in Two and Three Dimensions: Multicritical Bifurcation Versus Double Tricriticality-Endpoint
(Elsevier, 2023) Kecoglu, Ibrahim; Berker, Ahmet Nihat; Berker, A. Nihat
The global phase diagrams of the Ashkin-Teller model are calculated in d = 2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently improved Migdal-Kadanoff procedure. Three different ordered phases occur in the dimensionally distinct phase diagrams that reflect three-fold order-parameter permutation symmetry, a closed symmetry line, and a quasi-disorder line. First- and second-order phase boundaries are obtained. In d = 2, second-order phase transitions meeting at a bifurcation point are seen. In d = 3, first- and second-order phase transitions are separated by tricritical and critical endpoints.
Phase Transitions Between Different Spin-Glass Phases and Between Different Chaoses in Quenched Random Chiral Systems
(Amer Physical Soc., 2017) Çağlar, Tolga; Berker, Ahmet Nihat; Berker, A. Nihat
The left-right chiral and ferromagnetic-antiferromagnetic double-spin-glass clock model with the crucially even number of states q = 4 and in three dimensions d = 3 has been studied by renormalization-group theory. We find for the first time to our knowledge four spin-glass phases including conventional chiral and quadrupolar spin-glass phases and phase transitions between spin-glass phases. The chaoses in the different spin-glass phases and in the phase transitions of the spin-glass phases with the other spin-glass phases with the non-spin-glass ordered phases and with the disordered phase are determined and quantified by Lyapunov exponents. It is seen that the chiral spin-glass phase is the most chaotic spin-glass phase. The calculated phase diagram is also otherwise very rich including regular and temperature-inverted devil's staircases and reentrances.
Renormalization-Group Theory of the Heisenberg Model in D Dimensions
(Elsevier, 2022) Tunca, Egemen; Berker, Ahmet Nihat; Berker, A. Nihat
The classical Heisenberg model has been solved in spatial d dimensions, exactly in d = 1 and by the Migdal-Kadanoff approximation in d > 1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the specific heats are calculated in arbitrary dimension d. Fisher's exact result is recovered in d = 1. The absence of an ordered phase, conventional or algebraic (in contrast to the XY model yielding an algebraically ordered phase) is recovered in d = 2. A conventionally ordered phase occurs at d > 2. This method opens the way to complex-system calculations with Heisenberg local degrees of freedom.(c) 2022 Elsevier B.V. All rights reserved.
Nematic Phase of the N-Component Cubic-Spin Spin Glass in D=3: Liquid-Crystal Phase in a Dirty Magnet
(Elsevier, 2024) Artun, E. Can; Berker, Ahmet Nihat; Sarman, Deniz; Berker, A. Nihat
A nematic phase, previously seen in the n= 3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the-high temperature disordered phase, for number of components n >= 3, in spatial dimension n= 3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. This result is obtained from renormalization-group calculations that are exact on the hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. The nematic phase completely intervenes between the spin-glass phase and the disordered phase. The Lyapunov exponents of the spin-glass chaos are calculated from n= 1 up to n= 12 and show odd-even oscillations with respect to n.
First-order to second-order phase transition changeover and latent heats of q-state Potts models in d=2,3 from a simple Migdal-Kadanoff adaptation
(Amer Physical Soc, 2022) Berker, Ahmet Nihat; Berker, A. Nihat
The changeover from first-order to second-order phase transitions in q-state Potts models is obtained at q(c) = 2 in spatial dimension d = 3 and essentially at q(c) = 4 in d = 2, using a physically intuited simple adaptation of the Migdal-Kadanoff renormalization-group transformation. This simple procedure yields the latent heats at the first-order phase transitions. In both d = 2 and 3, the calculated phase transition temperatures, respectively compared with the exact self-duality and Monte Carlo results, are dramatically improved. The method, when applied to a slab of finite thickness, yields dimensional crossover.
Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals
(Pergamon-Elsevier Science Ltd, 2023) Artun, E. Can; Berker, Ahmet Nihat; Kecoglu, Ibrahim; Turkoglu, Alpar; Berker, A. Nihat
A complexity classification scheme is developed from the fractal spectra of spin-glass chaos and demonstrated with multigeographic multicultural music and brain electroencephalogram signals. Systematic patterns are found to emerge. Chaos under scale change is the essence of spin-glass ordering and can be obtained, contin-uously tailor-made, from the exact renormalization-group solution of Ising models on frustrated hierarchical lattices. The music pieces are from genres of Turkish music, namely Arabesque, Rap, Pop, Classical, and genres of Western music, namely Blues, Jazz, Pop, Classical. A surprising group defection occurs.
Across Dimensions: Two- and Three-Dimensional Phase Transitions From the Iterative Renormalization-Group Theory of Chains
(2020) Keçoğlu, İbrahim; Berker, Ahmet Nihat; Berker, A. Nihat
Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or nonzero magnetization, but the method reflects crossover from temperaturelike to fieldlike renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.
Frustrated Potts Model: Multiplicity Eliminates Chaos Via Reentrance
(Amer Physical Soc, 2020) Türkoğlu, Alpar; Berker, Ahmet Nihat; Berker, A. Nihat
The frustrated q-state Potts model is solved exactly on a hierarchical lattice, yielding chaos under rescaling, namely, the signature of a spin-glass phase, as previously seen for the Ising (q = 2) model. However, the ground-state entropy introduced by the (q > 2)-state antiferromagnetic Potts bond induces an escape from chaos as multiplicity q increases. The frustration versus multiplicity phase diagram has a reentrant (as a function of frustration) chaotic phase.