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Department: search.filters.department.Department of PhysicsSubject: search.filters.subject.Mathematical physics

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Now showing 1 - 10 of 27
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    Analytical solution of a stochastic content-based network model
    (Iop Publishing, 2005) Mungan, M; Balcan, D; Erzan, A; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854
    We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.
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    PublicationOpen Access
    Blume-Emery-Griffiths spin glass and inverted tricritical points
    (American Physical Society (APS), 2008) Özçelik, V. Ongun; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in d=3. The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricritical point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass regions, spin-glass and paramagnetic reentrances, and complete reentrance, where the spin-glass phase replaces the ferromagnet as temperature is lowered for all chemical potentials.
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    Constraining scalar-tensor theories using neutron star mass and radius measurements
    (American Physical Society (APS), 2022) Tuna, Semih; N/A; Department of Physics; Ünlütürk, Kıvanç İbrahim; Ramazanoğlu, Fethi Mübin; PhD Student; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 254225
    We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter ?? for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general.
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    PublicationOpen Access
    Deep spin-glass hysteresis-area collapse and scaling in the three-dimensional +/- J Ising model
    (American Physical Society (APS), 2012) Berker, A. Nihat; Department of Physics; Sarıyer, Ozan; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; N/A; 49854
    We investigate the dissipative loss in the +/- J Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate by means of frustration-preserving hard-spin mean-field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency omega(c) characterize the dependence on the sweep rate of the oscillating field. For omega < omega(c), the hysteresis area is equal to its value in the adiabatic limit omega = 0, while for omega > omega(c) it increases with the frequency through another randomness-dependent power law.
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    PublicationOpen Access
    Denaturation of circular DNA: supercoil mechanism 2011
    (American Physical Society (APS), 2011) Bar, Amir; Mukamel, David; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854
    The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the first-order transition displayed by the PS model for c > 2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the second-order transition found in the linear case in the regime 1 < c <= 2 disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.
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    PublicationOpen Access
    Denaturation of circular DNA: supercoils and overtwist
    (American Physical Society (APS), 2012) Bar, Amir; Mukamel, David; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854
    The denaturation transition of circular DNA is studied within a Poland-Scheraga-type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant κ associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c 2. For c > 2 and κ = 0 we find that the model exhibits a first-order transition. The transition becomes of higher order for any κ > 0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c.
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    Generalized unitarity relation for linear scattering systems in one dimension
    (Springer, 2019) Department of Physics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Physics; Department of Mathematics; College of Sciences; 4231
    We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, PT - symmetry, and transmission reciprocity.
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    High-precision thermodynamic and critical properties from tensor renormalization-group flows
    (American Physical Society (APS), 2008) Hinczewski, Michael; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.
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    PublicationOpen Access
    Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory
    (American Physical Society (APS), 2011) Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The roughening phase diagram of the d = 3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d = 2 Ising model for the full range of anisotropy, yielding no roughening transition.
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    PublicationOpen Access
    Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network
    (American Physical Society (APS), 2006) Hinczewski, Michael; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    We have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks-a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length center dot for p=0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562 500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from T-c. For p >= 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching T-c from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/root T-c-T) and exp(D/root T-c-T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.