Browsing by Author "Turkoglu, Alpar"

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Citation - WoS: 8
Citation - Scopus: 9
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; Electrical-Electronics Engineering
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.
Citation - WoS: 4
Citation - Scopus: 4
Phase Transitions of the Variety of Random-Field Potts Models
(Elsevier, 2021) Turkoglu, Alpar; Berker, Ahmet Nihat; Berker, A. Nihat; Electrical-Electronics Engineering
The phase transitions of random-field q-state Potts models in d = 3 dimensions are studied by renormalization-group theory by exact solution of a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions of a cubic lattice. The recursion, under rescaling, of coupled random-field and random-bond (induced under rescaling by random fields) coupled probability distributions is followed to obtain phase diagrams. Unlike the Ising model (q = 2), several types of random fields can be defined for q >= 3 Potts models, including random-axis favored, random-axis disfavored, random-axis randomly favored or disfavored cases, all of which are studied. Quantitatively very similar phase diagrams are obtained, for a given q for the three types of field randomness, with the low-temperature ordered phase persisting, increasingly as temperature is lowered, up to random-field threshold in d = 3, which is calculated for all temperatures below the zero-field critical temperature. Phase diagrams thus obtained are compared as a function of q. The ordered phase in the low-q models reaches higher temperatures, while in the high-q models it reaches higher random fields. This renormalization-group calculation result is physically explained. (c) 2021 Elsevier B.V. All rights reserved.
XY-Ashkin Phase Diagram in D=3
(Elsevier, 2025) Turkoglu, Alpar; Berker, A. Nihat
The phase diagram of the Ashkin-Tellerized XY model in spatial dimension d = 3 is calculated by renormalization-group theory. In this system, each site has two spins, each spin being an XY spin, that is having orientation continuously varying in 2 pi radians. Nearest-neighbor sites are coupled by two-spin and four-spin interactions. The phase diagram has ordered phases that are ferromagnetic and antiferromagnetic in each of the spins, and phases that are ferromagnetic and antiferromagnetic in the multiplicative spin variable. The phase diagram distinctively exhibits a pair of symmetrically situated direct bifurcation points and a pair of symmetrically situated reverse bifurcation points of the phase boundaries. The renormalization-group flows are in terms of the doubly composite Fourier coefficients of the exponentiated energy of nearest-neighbor spins.