Researcher:
Berker, Ahmet Nihat

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Ahmet Nihat

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Berker

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Berker, Ahmet Nihat

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2005 - 2009152010 - 20164

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    Two superconducting phases in the d=3 hubbard model - phase diagram and specific heat from renormalization-group calculations.
    (Springer, 2005) Hinczewski, M.; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences; 179795
    The phase diagram of the d=3 Hubbard model is calculated as a function of temperature and electron density < n(i)>, in the full range of densities between 0 and 2 electrons per site, using renormalization-group theory. An antiferromagnetic phase occurs at lower temperatures, at and near the half-filling density of < n(i)> = 1. The antiferromagnetic phase is unstable to hole or electron doping of at most 15%, yielding to two distinct"tau" phases: for large coupling U/t, one such phase occurs between 30-35% hole or electron doping, and for small to intermediate coupling U/t another such phase occurs between 10-18% doping. Both tau phases are distinguished by non-zero hole or electron hopping expectation values at all length scales. Under further doping, the tau phases yield to hole- or electron-rich disordered phases. We have calculated the specific heat over the entire phase diagram. The low-temperature specific heat of the weak-coupling tau phase shows an exponential decay, indicating a gap in the excitation spectrum, and a CUSP singularity at the phase boundary. The strong-coupling tau phase, on the other hand, has a critical exponent alpha approximate to-1, and an additional peak in the specific heat above the transition temperature possibly indicating pair formation. In the limit of large Coulomb repulsion, the phase diagram of the tJ model is recovered.
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    D=3 anisotropic and d=2 tj models: phase diagrams, thermodynamic properties, and chemical potential shift
    (Springer, 2006) Hinczewski, M.; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences; 179795
    The anisotropic d=3 tJ model is studied by renormalization-group theory, yielding the evolution of the system as interplane coupling is varied from the isotropic three-dimensional to quasi-two-dimensional regimes. Finite-temperature phase diagrams, chemical potential shifts, and in-plane and interplane kinetic energies and antiferromagnetic correlations are calculated for the entire range of electron densities. We find that the novel tau phase, seen in earlier studies of the isotropic d=3 tJ model, persists even for strong anisotropy. While the tau phase appears at low temperatures at 30-35% hole doping away from [n(i)]=1, at smaller hole dopings we see a complex lamellar structure of antiferromagnetic and disordered regions, with a suppressed chemical potential shift, a possible marker of incommensurate ordering in the form of microscopic stripes. An investigation of the renormalization-group flows for the isotropic two-dimensional tJ model also shows a clear pre-signature of the tau phase, which in fact appears with finite transition temperatures upon addition of the smallest interplane coupling.
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    PublicationOpen Access
    Field-driven hysteresis of the d=3 Ising spin glass: hard-spin mean-field theory
    (American Physical Society (APS), 2007) Yücesoy, Burcu; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    Hysteresis loops are obtained in the Ising spin-glass phase in d=3 using frustration-conserving hard-spin mean-field theory. The system is driven by a time-dependent random magnetic field H-Q that is conjugate to the spin-glass order Q, yielding a field-driven first-order phase transition through the spin-glass phase. The hysteresis loop area A of the Q-H-Q curve scales with respect to the sweep rate h of magnetic field as A-A(0)similar to h(b). In the spin-glass and random-bond ferromagnetic phases, the sweep-rate scaling exponent b changes with temperature T but appears not to change with antiferromagnetic bond concentration p. By contrast, in the pure ferromagnetic phase, b does not depend on T and has a sharply different value than in the two other phases.
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    PublicationOpen Access
    Phase separation and charge-ordered phases of the d=3 Falicov-Kimball model at nonzero temperature: temperature-density-chemical potential global phase diagram from renormalization-group theory
    (American Physical Society (APS), 2011) Hinczewski, Michael; Department of Physics; Sarıyer, Ozan; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.
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    PublicationOpen Access
    Multicritical points for spin-glass models on hierarchical lattices
    (American Physical Society (APS), 2008) Ohzeki, Masayuki; Nishimori, Hidetoshi; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.
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    PublicationOpen Access
    Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in the d=3 t-J model: finite-temperature global phase diagrams from renormalization group theory
    (American Physical Society (APS), 2009) Hinczewski, Michael; Department of Physics; Kaplan, C. Nadir; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The renormalization-group theory of the d=3 t-J model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, further/first-neighbor interaction-strength ratios. With the inclusion of further-neighbor interactions, an extremely rich phase diagram structure is found and is explained by competing and frustrated interactions. In addition to the tau(tJ) phase seen in earlier studies of the nearest-neighbor d=3 t-J model, the tau(Hb) phase seen before in the d=3 Hubbard model appears both near and away from half filling.
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    PublicationOpen Access
    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
    Quenched-vacancy induced spin-glass order
    (American Physical Society (APS), 2009) Gülpınar, Gül; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    The ferromagnetic phase of an Ising model in d=3, with any amount of quenched antiferromagnetic bond randomness, is shown to undergo a transition to a spin-glass phase under sufficient quenched bond dilution. This result, demonstrated here with the numerically exact global renormalization-group solution of a d=3 hierarchical lattice, is expected to hold true generally, for the cubic lattice and for quenched site dilution. Conversely, in the ferromagnetic-spin-glass-antiferromagnetic phase diagram, the spin-glass phase expands under quenched dilution at the expense of the ferromagnetic and antiferromagnetic phases. In the ferromagnetic-spin-glass phase transition induced by quenched dilution, reentrance as a function of temperature is seen, as previously found in the ferromagnetic-spin-glass transition induced by increasing the antiferromagnetic bond concentration.
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    Strong violation of critical phenomena universality: Wang-Landau study of the two-dimensional Blume-Capel model under bond randomness
    (American Physical Society (APS), 2009) Malakis, A.; Hadjiagapiou, I. A.; Fytas, N. G.; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of Sciences
    We study the pure and random-bond versions of the square lattice ferromagnetic Blume-Capel model, in both the first-order and second-order phase transition regimes of the pure model. Phase transition temperatures, thermal and magnetic critical exponents are determined for lattice sizes in the range L=20-100 via a sophisticated two-stage numerical strategy of entropic sampling in dominant energy subspaces, using mainly the Wang-Landau algorithm. The second-order phase transition, emerging under random bonds from the second-order regime of the pure model, has the same values of critical exponents as the two-dimensional Ising universality class, with the effect of the bond disorder on the specific heat being well described by double-logarithmic corrections, our findings thus supporting the marginal irrelevance of quenched bond randomness. On the other hand, the second-order transition, emerging under bond randomness from the first-order regime of the pure model, has a distinctive universality class with nu=1.30(6) and beta/nu=0.128(5). These results amount to a strong violation of universality principle of critical phenomena, since these two second-order transitions, with different sets of critical exponents, are between the same ferromagnetic and paramagnetic phases. Furthermore, the latter of these two sets of results supports an extensive but weak universality, since it has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional systems with and without quenched disorder. In the conversion by bond randomness of the first-order transition of the pure system to second order, we detect, by introducing and evaluating connectivity spin densities, a microsegregation that also explains the increase we find in the phase transition temperature under bond randomness.