Browsing by Author "Berker, A. Nihat"

Now showing 1 - 20 of 27

Citation Count: 1
Across Dimensions: Two- and Three-Dimensional Phase Transitions From the Iterative Renormalization-Group Theory of Chains
(2020) Keçoğlu, İbrahim; 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.
Citation Count: 4
Asymmetric Phase Diagrams, Algebraically Ordered Berezinskii-Kosterlitz Phase, and Peninsular Potts Flow Structure in Long-Range Spin Glasses
(Amer Physical Soc, 2022) Gurleyen, S. Efe; Berker, A. Nihat
The Ising spin-glass model on the three-dimensional (d = 3) hierarchical lattice with long-range ferromagnetic or spin-glass interactions is studied by the exact renormalization-group solution of the hierarchical lattice. The chaotic characteristics of the spin-glass phases are extracted in the form of our calculated, in this case continuously varying, Lyapunov exponents. Ferromagnetic long-range interactions break the usual symmetry of the spin-glass phase diagram. This phase-diagram symmetry breaking is dramatic, as it is underpinned by renormalization-group peninsular flows of the Potts multicritical type. A Berezinskii-Kosterlitz-Thouless (BKT) phase with algebraic order and a BKT-spin-glass phase transition with continuously varying critical exponents are seen. Similarly, for spin-glass long-range interactions, the Potts mechanism is also seen, by the mutual annihilation of stable and unstable fixed distributions causing the abrupt change of the phase diagram. On one side of this abrupt change, two distinct spin-glass phases, with finite (chaotic) and infinite (chaotic) coupling asymptotic behaviors are seen with a spin-glass to spin-glass phase transition.
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
Covid-19 Modeling Based on Real Geographic and Population Data
(Tubitak Scientific & Technological Research Council Turkey, 2023) Baysazan, Emir; Berker, A. Nihat; Mandal, Hasan; Kaygusuz, Hakan
Background/aim: Intercity travel is one of the most important parameters for combating a pandemic. The ongoing COVID-19 pandemic has resulted in different computational studies involving intercity connections. In this study, the effects of intercity connections during an epidemic such as COVID-19 are evaluated using a new network model. Materials and methods: This model considers the actual geographic neighborhood and population density data. This new model is applied to actual Turkish data by means of provincial connections and populations. A Monte Carlo algorithm with a hybrid lattice model is applied to a lattice with 8802 data points. Results: Around Monte Carlo step 70, the number of active cases in Turkiye reaches up to 8.0% of the total population, which is followed by a second wave at around Monte Carlo step 100. The number of active cases vanishes around Monte Carlo step 160. Starting with Istanbul, the epidemic quickly expands between steps 60 and 100. Simulation results fit the actual mortality data in Turkiye. Conclusion: This model is quantitatively very efficient in modeling real-world COVID-19 epidemic data based on populations and geographical intercity connections, by means of estimating the number of deaths, disease spread, and epidemic termination.
Citation Count: 9
Devil'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. Nihat
The 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.
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: 3
The Effect of Weekend Curfews on Epidemics: a Monte Carlo Simulation
(Tubitak Scientific & Technical Research Council Turkey, 2021) Kaygusuz, Hakan; Berker, A. Nihat
The ongoing COVID-19 pandemic is being responded with various methods, applying vaccines, experimental treatment options, total lockdowns or partial curfews. Weekend curfews are among the methods for reducing the number of infected persons, and this method is practically applied in some countries such as Turkey. In this study, the effect of weekend curfews on reducing the spread of a contagious disease, such as COVID-19, is modeled using a Monte Carlo algorithm with a hybrid lattice model. In the simulation setup, a fictional country with three towns and 26,610 citizens were used as a model. Results indicate that applying a weekend curfew reduces the ratio of ill cases from 0.23 to 0.15. The results also show that applying personal precautions such as social distancing is important for reducing the number of cases and deaths. If the probability of disease spread can be reduced to 0.1, in that case, the death ratio can be minimized down to 0.
Citation Count: 3
Electric-field induced phase transitions in capillary electrophoretic systems
(Aip Publishing, 2021) Kaygusuz, Hakan; Erim, F. Bedia; Berker, A. Nihat
The movement of particles in a capillary electrophoretic system under electroosmotic flow was modeled using Monte Carlo simulation with the Metropolis algorithm. Two different cases with repulsive and attractive interactions between molecules were taken into consideration. Simulation was done using a spin-like system, where the interactions between the nearest and second closest neighbors were considered in two separate steps of the modeling study. A total of 20 different cases with different rates of interactions for both repulsive and attractive interactions were modeled. The movement of the particles through the capillary is defined as current. At a low interaction level between molecules, a regular electroosmotic flow is obtained; on the other hand, with increasing interactions between molecules, the current shows a phase transition behavior. The results also show that a modular electroosmotic flow can be obtained for separations by tuning the ratio between molecular interactions and electric field strength.
Citation Count: 8
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) Devre, H. Yagiz; 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.
Citation Count: 0
Fractal Measures of Sea, Lake, Strait, and Dam-Reserve Shores: Calculation, Differentiation, and Interpretation
(ELSEVIER, 2021) Yılmazer, Dilara; Berker, A. Nihat; Yılmaz, Yücel
The fractal dimensions d(f) of the shore lines of the Mediterranean, the Aegean, the Black Sea, the Bosphorus Straits (on both the Asian and European sides), the Van Lake, and the lake formed by the Ataturk Dam have been calculated. Important distinctions have been found and explained. (C) 2021 Elsevier B.V. All rights reserved.
Citation Count: 3
Frustrated Potts Model: Multiplicity Eliminates Chaos Via Reentrance
(Amer Physical Soc, 2020) Türkoğlu, Alpar; 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.
Citation Count: 0
Global Ashkin-Teller Phase Diagrams in Two and Three Dimensions: Multicritical Bifurcation Versus Double Tricriticality-Endpoint
(Elsevier, 2023) Kecoglu, Ibrahim; 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.
Citation Count: 6
Lower Critical Dimension of the Random-Field Xy Model and the Zero-Temperature Critical Line
(Amer Physical Soc, 2022) Akin, Kutay; Berker, A. Nihat
The random-field XY model is studied in spatial dimensions d = 3 and 4, and in between, as the limit q -> infinity of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower critical dimension is determined between 3.81 < d(c) < 4. When the random field is scaled with q, a line segment of zero-temperature criticality is found in d = 3. When the random field is scaled with q(2), a universal phase diagram is found at intermediate temperatures in d = 3.
Citation Count: 13
Lower Lower-Critical Spin-Glass Dimension From Quenched Mixed-Spatial Spin Glasses
(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. Nihat
By 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.)
Citation Count: 2
Maximally Random Discrete-Spin Systems With Symmetric and Asymmetric Interactions and Maximally Degenerate Ordering
(Amer Physical Soc., 2018) Atalay, Bora; Berker, A. Nihat
Discrete-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.
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: 1
Metastable 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. Nihat
Metastable 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.
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.