Browsing by Author "Artun, E. Can"

Now showing 1 - 8 of 8

Citation Count: 0
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) Artun, E. Can; 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.
Citation Count: 9
Complete Density Calculations of Q-State Potts and Clock Models: Reentrance of Interface Densities Under Symmetry Breaking
(Amer Physical Soc, 2020) Artun, E. Can; Berker, A. Nihat
All local bond-state densities are calculated for q-state Potts and clock models in three spatial dimensions, d = 3. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion relations, and simultaneously are the Migdal-Kadanoff approximation for the cubic lattice. Reentrant behavior is found in the interface densities under symmetry breaking, in the sense that upon lowering the temperature, the value of the density first increases and then decreases to its zero value at zero temperature. For this behavior, a physical mechanism is proposed. A contrast between the phase transition of the two models is found and explained by alignment and entropy, as the number of states q goes to infinity. For the clock models, the renormalization-group flows of up to 20 energies are used.
Citation Count: 1
Driven and Non-Driven Surface Chaos in Spin-Glass Sponges
(Pergamon-elsevier Science Ltd, 2023) Pektas, Yigit Ertac; 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.
Citation Count: 0
Merged Potts-Clock Model: Algebraic and Conventional Multistructured Multicritical Orderings in Two and Three Dimensions
(Amer Physical Soc, 2023) Artun, E. Can; Berker, A. Nihat
A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d = 2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first-and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.
Citation Count: 0
Metastable Potts droplets
(AMER PHYSICAL SOC, 2021-03) Artun, E. Can; Berker, A. Nihat
The existence and limits of metastable droplets have been calculated using finite-system renormalization-group theory, for q-state Potts models in spatial dimension d = 3. The dependence of the droplet critical sizes on magnetic field, temperature, and number of Potts states q has been calculated. The same method has also been used for the calculation of hysteresis loops across first-order phase transitions in these systems. The hysteresis loop sizes and shapes have been deduced as a function of magnetic field, temperature, and number of Potts states q. The uneven appearance of asymmetry in the hysteresis loop branches has been noted. The method can be extended to criticality and phase transitions in metastable phases, such as in surface-adsorbed systems and water.
Citation Count: 4
Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals
(Pergamon-Elsevier Science Ltd, 2023) Artun, E. Can; 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.
Citation Count: 0
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; 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.
Citation Count: 1
Spin-S Spin-Glass Phases in the D=3 Ising Model
(Amer Physical Soc, 2021) Artun, E. Can; Berker, A. Nihat
All higher-spin (s >= 1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d = 3, exactly on a d = 3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d = 3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s -> infinity. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of lambda = 1.93 and runaway exponent of y(R) = 0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at p(t) = 0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.