Elektrik - Elektronik Mühendisliği Bölümü Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12469/47
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Browsing Elektrik - Elektronik Mühendisliği Bölümü Koleksiyonu by Institution Author "Berker, A. Nihat"
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Article Citation - WoS: 1Citation - Scopus: 1Across Dimensions: Two- and Three-Dimensional Phase Transitions From the Iterative Renormalization-Group Theory of Chains(2020) Keçoğlu, İbrahim; Berker, A. NihatSharp 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.Article Citation - WoS: 9Citation - Scopus: 9Complete 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. NihatAll 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.Article Citation - WoS: 11Citation - Scopus: 11Devil's Staircase Continuum in the Chiral Clock Spin Glass With Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions(Amer Physical Soc., 2017) Caglar, Tolga; Berker, A. NihatThe chiral clock spin-glass model with q = 5 states with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations is studied in d = 3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature antiferromagnetic bond concentration p random chirality strength and right-chirality concentration c. The system has a ferromagnetic phase a multitude of different chiral phases a chiral spin-glass phase and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase bordered by fragments of regular and temperature-inverted devil's staircases are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.Article Citation - WoS: 3Citation - Scopus: 3Frustrated Potts Model: Multiplicity Eliminates Chaos Via Reentrance(Amer Physical Soc, 2020) Türkoğlu, Alpar; Berker, A. NihatThe 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.Article Citation - WoS: 14Citation - Scopus: 14Lower Lower-Critical Spin-Glass Dimension From Quenched Mixed-Spatial Spin Glasses(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. NihatBy quenched-randomly mixing local units of different spatial dimensionalities we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1 <= d <= 3. The global phase diagram in temperature antiferromagnetic bond concentration and spatial dimensionality is calculated. We find that as dimension is lowered the spin-glass phase disappears to zero temperature at the lower-critical dimension d(c) = 2.431. Our system being a physically realizable system this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards d(c) the spin-glass critical temperature continuously goes to zero but the spin-glass chaos fully subsists to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent measuring the strength of chaos is thus largely unaffected by the approach to d and shows a discontinuity to zero at d(c.)Article Citation - WoS: 2Citation - Scopus: 2Maximally Random Discrete-Spin Systems With Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. NihatDiscrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric ferromagnetic or antiferromagnetic including off-diagonal disorder are studied for the number of states q = 34 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d > 1 and all nonmfimte temperatures the system eventually renormalizes to a random single state thus signaling q x q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus a temperature range of short-range disorder in the presence of long-range order is identified as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures behaves similarly for ferromagnetic and antiferromagnetic interactions and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1 + epsilon the system is as expected disordered at all temperatures for d = 1.Article Citation - WoS: 1Citation - Scopus: 1Metastable Reverse-Phase Droplets Within Ordered Phases: Renormalization-Group Calculation of Field and Temperature Dependence of Limiting Size(AMER PHYSICAL SOC, 2020) Eren, Ege; Berker, A. NihatMetastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase and noting whether the reverse-phase magnetization sustains. The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of temperature and magnetic field for the Ising model in three dimensions. The method also yields hysteresis loops for finite systems, as function of temperature and system size.Article Citation - WoS: 12Citation - Scopus: 12Phase Transitions Between Different Spin-Glass Phases and Between Different Chaoses in Quenched Random Chiral Systems(Amer Physical Soc., 2017) Çağlar, Tolga; Berker, A. NihatThe 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.
