PhD Dissertation-Efe İlker
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Differentiated Chaos in Phases and Phase Boundaries, Overfrustrated/Underfrustrated Repressed/Induced Spin-Glass Order, Asymmetric Phase Diagrams, and Critical Phases in Spin-Glass Systems




Efe İlker
,  PhD Dissertation, 2015


Thesis Jury

Prof. Dr. A. Nihat Berker (Thesis Advisor),

Prof. Dr. Sondan Durukanoğlu Feyiz,

Prof. Dr. Ali Rana Atılgan,

Assoc. Prof. Alkan Kabakçıoğlu,

Prof. Dr. Haluk Özbek



Date & Time: 24.07.2015 –  9.00 AM

Place: FENS L061

Keywords : Spin-glass and other random models, Renormalization-group theory,

 Statistical mechanics of model systems




Spin-glass problems continue to fascinate with new orderings and phase diagrams under frustration and ground-state entropy. In this thesis, new types of spin-glass systems are introduced resulting in a rich information on these complex structures and novel orderings. We realized that in spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d = 3 and d = 2 are studied by a detailed renormalization-group analysis. A variety of information about the effects of frustration in spin-glass systems is obtained including evolution of phase diagrams, destroyal of orderings, chaotic rescaling behavior, and thermodynamic properties. Our results are suggestive for hypercubic lattices.


Furthermore, spin-glass phases and phase transitions for q-state clock models and their q → ∞ limit the XY model, in spatial dimension d = 3, are studied. For even q, in addition to the now well established chaotic rescaling behavior of the spin-glass phase, each of the two types of spin-glass phase boundaries displays, under renormalization-group trajectories, their own distinctive chaotic behavior. We thus characterize each different phase and phase boundary exhibiting chaos by its distinct Lyapunov exponent, which we calculate. We show that, under renormalization group, chaotic trajectories and fixed distributions are mechanistically and quantitatively equivalent. The phase diagrams for arbitrary even q, for all non-infinite q, have a finite-temperature spin-glass phase. In addition to that, the spin-glass phases and the spinglass-paramagnetic phase boundaries exhibit universal fixed distributions, chaotic trajectories and Lyapunov exponents, independent of q. In the XY model limit, our calculations indicate a zero-temperature spin-glass phase.

On the other hand, very distinctive orderings and phase diagram structures are found for odd q. These models exhibit asymmetric phase diagrams, as is also the case for quantum Heisenberg spin-glass models. No finite-temperature spin-glass phase occurs. For all odd q ≥ 5, algebraically ordered antiferromagnetic phases occur. All algebraically ordered phases have the same structure, determined by an attractive finite-temperature sink fixed point where a dominant and a subdominant pair states have the only non-zero Boltzmann weights. The phase transition critical exponents quickly saturate to the high q value.

Finally, as a part of the thesis, the diffusive dynamics on non-equilibrium systems are discussed. In general, the effects of microlevel motions are observed indirectly in the macroworld, hence observables that are less sensitive to microlevel randomness can be obtained with fewer parameters. MD simulations are extensively used on the investigation of many body systems or specific molecules interacting with many body environment under the effect of thermodynamics. With a sincere interest on these studies, we work on two different problems. In the first study, we demonstrate a scheme projecting continuous dynamical modes on to a discrete Markov State Model (MSM) and analyze cw-ESR spectrum of a spin label attached to a macromolecule undergoing an arbitrary (but Markovian) rotational diffusion. In the second study, we generate the statistics and calculate the energetics of the dominant surface diffusion mechanisms and observe growth modes on nanoscale bimetallic synthesis.