Browsing by Subject "Critical phenomena"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item Open Access Logistic cellular automata(Bilkent University, 2019-09) Ibrahimi, MuhametCellular Automata (CA), initially formalized to investigate self-reproducing constructions, are among the most frequently used tools to model and understand complex systems. These computational frameworks are de ned in discrete spacetime- state domains, where time evolution occurs through local interactions. Despite the simple properties and the succinct absence of long range connections, these implementations have been proven proper for studying large scale collective behavior and self-organizing mechanisms which often emerge in dynamical systems. Following the spirit of the well-known Logistic Map, we introduce a single parameter that tunes the dynamics of totalistic CA by mapping their discrete state space into a Cantor set. By introducing this simple approach on two archetypal models, this study addresses further investigation of several complex phenomena: critical deterministic phase transitions, pattern formation and tunable emanation of self-organized morphologies in these discrete domains. We rst apply this approach to Conway's Game of Life and observe sudden changes in asymptotic dynamics of the system accompanied by emergence of complex propagators. Incorporation of the new state space with system features is used to explain the critical points and formulate the tuning parameter range where the propagators adaptively survive, by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, a totalistic elementary one-dimensional CA. In addition, the latter case shows that transitions between Wolfram's universality classes of CA can be achieved by tuning a single parameter continuously. Finally, we implement the same idea in other models and qualitatively report the expanding complexity that these frameworks support.Item Open Access Phase transitions and renormalization-group theory(1989-07) Berker, A. NihatThe study of critical phenomena targets the qualitatively new phenomena that occur through the interactions of very large numbers of degrees of freedom. Such situations are typically realized near the onset of the transition between two thermodynamic phases. The special challenge of this field is thus due to the truly many-body nature of its subject. Another motivating challenge of the field has been the feasibility of immediate comparisons between the outcomes of sophisticated experiments and sophisticated theories, especially in condensed matter systems. Adding to this the wide variety of experimental and theoretical methods, it is seen that many cultures meet and exchange under the aegis of critical phenomena and phase transitions, contributing to the dynamism and intellectual enrichment of the field.Item Open Access Quantum phase transitions from analysis of the polarization amplitude(American Physical Society, 2019) Hetenyi, Balazs; Dora, B.In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a discretized characteristic function and derive formulas for its cumulants and moments. In the case of a noninteracting system, our scheme leads to the gauge-invariant cumulants known from polarization theory. We study the behavior of such cumulants for several interacting models. In a one-dimensional system of spinless fermions with nearest neighbor interaction the transition at which gap closure occurs can be clearly identified from the finite size scaling exponent of the variance. When next nearest neighbor interactions are turned on a model with a richer phase diagram emerges, but the finite size scaling exponent is still an effective way to identify the localization transition.Item Open Access Scaling and renormalization in the modern theory of polarization: application to disordered systems(American Physical Society, 2021-12-15) Hetényi, Balázs; Parlak, Selçuk; Yahyavi, MohammadWe develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension, the renormalized disorder strength tends to infinity, indicating the entire absence of extended states. Zero (infinite) disorder is a repulsive (attractive) fixed point. In two and three dimensions, at small system sizes, two additional fixed points appear, both at finite disorder: Wa(Wr) is attractive (repulsive) such that WaItem Open Access Synthesis of V2 O3 nanoplates for the exploration of the correlated supercritical state(American Physical Society, 2019) Rasouli, Hamid Reza; Mehmood, Naveed; Çakıroğlu, Onur; Sürmeli, Engin Can; Kasırga, T. SerkanPeculiar features exist in the stress-temperature phase stability diagram of V2O3, such as a first-order phase transition between the paramagnetic insulating and metallic phases that ends with a critical point, quantum phase transition, and a triple point. These features remain largely unexplored, and the exact nature of the phase transitions is not clear due to very limited control over the stress in bulk or film samples. Here, we show the synthesis of single-crystal V2O3 nanoplates using chemical vapor deposition via van der Waals epitaxy. Thickness of the V2O3 nanoplates range from a few to hundreds of nanometers, and they can be mechanically exfoliated from the growth substrate. Using Raman spectroscopy on the nanoplates, we reveal that, upon heating, V2O3 enters a supercritical state for both tensile strained and relaxed crystals with a similar out-of-plane response. Transmission electron microscopy on V2O3 nanoplates hints at the existence of a structural change when the crystals are heated. Our results show that V2O3nanoplates should be useful for studying the physics of the supercritical state and the phase stability of V2O3 to enable new horizons in applications.