arXiv subjects

Ibrahim Kecoglu

Publications and source records attributed to Ibrahim Kecoglu.

3 recordsLinked to original sources

arXiv2025

Global Ashkin-Teller Phase Diagrams in Two and Three Dimensions: Multicritical Bifurcation versus Double Tricriticality Endpoint

The global phase diagrams of the Askin-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.

cond-mat.stat-mech↗

arXiv2022

Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals

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, continuously tailor-made, from the exact renormalization-group solution of Ising models on frustrated hierarchical lattices. The music pieces are from Turkish music, namely Arabesque, Rap, Pop, Classical, and Western music, namely Blues, Jazz, Pop, Classical. A surprising group defection occurs.

cond-mat.dis-nn↗

arXiv2020

Across Dimensions: Two- and Three-Dimensional Phase Transitions from the Iterative Renormalization-Group Theory of Chains

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 non-zero magnetization, but the method reflects crossover from temperature-like to field-like 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.

cond-mat.stat-mech↗