Nonuniversal Behavior Research Articles

A model for the dependence of the electrical conductance with the applied stress in insulating-conducting composites

A model for the dependence of the electrical conductance, G, with the strain induced by external mechanical stress in conducting particles-polymer composites is presented. The model assumes that the percolation probability between neighboring particles must depart from a scale-invariant behavior but saturate at moderated-high strains, reaching percolation path’s saturation, with sigmoid dependence. This dependence is obtained by proposing a dynamic picture where contacts or bonds between neighboring particles are created but also destructed when a stress is applied and relatively moderated or high strains, ε, are produced in the composite. The electrical conductance of prepared graphite-polydimethylsiloxane composites were measured as function of the applied pressure and fitted by the presented model. The elastic response to the uniaxial compression was studied using a texture analyzer. The possibility of nonuniversal effects in the conduction critical exponent, t, was taken into account. It is concluded that the saturation of the response in the G versus ε plots cannot be assigned to nonuniversal behavior of the exponent t, or to saturation of the elastic response. On the other hand, the presented model accounts for all the main experimental features observed in these systems and for previously reported data of elastomer composites. The simulated behavior of the piezoresistivity coefficient is also in qualitative agreement with previous reports.

Low-dimensional weakly interacting Bose gases: Nonuniversal equations of state

The zero-temperature equation of state is analyzed in low-dimensional bosonic systems. We propose to use the concept of energy-dependent $s$-wave scattering length for obtaining estimations of nonuniversal terms in the energy expansion. We test this approach by making a comparison to exactly solvable one-dimensional problems and find that the generated terms have the correct structure. The applicability to two-dimensional systems is analyzed by comparing with results of Monte Carlo simulations. The prediction for the nonuniversal behavior is qualitatively correct and the densities, at which the deviations from the universal equation of state become visible, are estimated properly. Finally, the possibility of observing the nonuniversal terms in experiments with trapped gases is also discussed.

Non-universal finite-size scaling of rough surfaces

We demonstrate the non-universal behavior of finite-size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in a generalized point of view. In particular, we show the violation of the universal nature of the scaling function corresponding to the height fluctuation in (1+1) dimension. The second-order moment of the height fluctuation shows three distinct crossover regions separated by two crossover timescales namely, t×1 and t×2. Each regime has different scaling properties. The overall scaling behavior is postulated with a new scaling relation represented as the linear sum of two scaling functions valid for each scaling regime. Besides, we note the dependence of the roughness exponents on the finite size of the system. The roughness exponents corresponding to the rough surface is compared with the growth rate or the velocity of the surface.

Nonuniversal behavior of cold Fermi condensates with narrow Feshbach resonances

In this paper we construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a narrow Feshbach resonance. We show how, from first principles, it permits a hydrodynamic description of the BEC-BCS crossover from which the equation of state, intimately related to the speed of sound, can be derived. Specifically, we stress the non-universal behaviour of the equation of state at the unitary limit of infinite scattering length that arises when either, or both, of the range of the inter-atomic force and the scale of the molecular field become large.

Patchy percolation on a hierarchical network with small-world bonds

The bond-percolation properties of the recently introduced Hanoi networks are analyzed with the renormalization group. Unlike scale-free networks, these networks are meant to provide an analytically tractable interpolation between finite-dimensional, lattice-based models and their mean-field limits. In percolation, the hierarchical small-world bonds in the Hanoi networks impose order by uniting otherwise disconnected, local clusters. This "patchy" order results in merely a finite probability to obtain a spanning cluster for certain ranges of the bond probability, unlike the usual 0-1 transition found on ordinary lattices. The various networks studied here exhibit a range of phase behaviors, depending on the prevalence of those long-range bonds. Fixed points in general exhibit nonuniversal behavior.

Spin Hall Effect in Symmetric Wells with Two Subbands

We investigate the spin Hall conductivity σxyz of a clean 2D electron gas formed in a two-subband well. We determine σxyz as arising from the inter-subband induced spin–orbit (SO) coupling η (Calsaverini et al., Phys. Rev. B 78:155313, 2008) via a linear-response approach due to Rashba. By self-consistently calculating η for realistic wells, we find that σxyz presents a non-monotonic (and non-universal) behavior and a sign change as the Fermi energy varies between the subband edges. Although our σxyz is very small (i.e., ≪``e/4π″), it is non-zero as opposed to linear-in-k SO models.

Method to modify random matrix theory using short-time behavior in chaotic systems

We discuss a modification to random matrix theory (RMT) eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard RMT and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations and show how the approach leads to a significant improvement in the accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.

Finite-size scaling in band ferromagnets with non-universal critical behavior

The ultra-high sensitivity of the ferromagnetic resonance (FMR) techniquehas been fully exploited to study the finite-size effects in the criticalregion near the ferromagnetic to paramagnetic phase transition inCr75−xFe25+x (x = 0, 5) thin films of high structural and magnetic quality. Conclusiveexperimental evidence is provided for the validity of finite-size scaling.Irrespective of the film thickness and composition, the critical exponentsβ,γ andν for spontaneous magnetization, initial magnetic susceptibility and spin–spin correlationlength retain their bulk values so that no dimensionality crossover occurs within the filmthickness range covered in the FMR experiments. The present results indicate that (i) likeCr75−xFe25+x, the previously studiedFe, Co, Ni, and CoNi3 thin films behave as itinerant-electron (band) ferromagnets inwhich the isotropic long-range interactions between spins decay asJ(r)∼r−(d+σ) (σ>0), and (ii) the latticedimensionality d,spin dimensionality m, and range of spin–spin interactions (via the material-specific parameterσ) decide the (non-universal) values of the critical exponents.

A brief description to different multi-fractal behaviors of daily wind speed records over China

Scaling behaviors of the long daily wind speed records of four selected weather stations over China were analyzed by using Multi-Fractal Detrended Fluctuation Analysis (MF-DFA). The results indicated that all these four stations are characterized by long-range power-law correlations, but MF-DFA results showed non-universal multi-fractal behaviors over China. We fitted generalized Hurst exponent h ( q ) via a modified generalized binomial multiplicative cascade model, and different widths of the multi-fractal spectrum are estimated.

Theoretical studies of spin-dependent electronic transport in ferromagnetically contacted graphene flakes

Based on a tight-binding model and a recursive Green's function technique, spin-dependent ballistic transport through tiny graphene sheets (flakes) is studied. The main interest is focused on electrical conductivity, giant magnetoresistance (GMR), and shot noise. It is shown that when graphene flakes are sandwiched between two ferromagnetic electrodes, the resulting GMR coefficient may be quite significant. This statement holds true both for zigzag and armchair chiralities, as well as for different aspect (width/length) ratios. Remarkably, in absolute values the GMR of the armchair-edge graphene flakes is systematically greater than that corresponding to the zigzag-edge graphene flakes. This finding is attributed to the different degree of conduction channel mixing for the two chiralities in question. It is also shown that for big aspect ratio flakes, three-dimensional end-contacted leads, very much like invasive contacts, result in nonuniversal behavior of both conductivity and Fano factor.

Shubnikov–de Haas effect in n-CdSb:In under pressure

Magnetoresistance (MR) of single crystals of the group II–V semiconductor n-CdSb doped with In is investigated in magnetic fields B up to 7 T and temperatures T between 1.2 and 2.4 K under hydrostatic pressure p = 0–10 kbar. Shubnikov–de Haas (SdH) oscillations of MR observed up to B ∼ 4 T are characterized by a single period, giving evidence for one participating group of conduction band electrons. Pressure dependence of the SdH period and concentration reveal a second group of charge carriers, connected to a resonance impurity band with delocalized states. The SdH amplitude, A, exhibits non-universal behavior attributable to its sensitivity to scattering mechanism at low quantum numbers. The parameters characterizing the non-universality of A(T) and the pressure dependence of the cyclotron effective mass, mc(p), and of the concentration of conduction electrons, nSdH, are given. The dependences of mc and the Fermi energy on pressure are consistent with Kane-type non-parabolicity of the conduction band.

Fermion mass hierarchy from the soft wall

We develop a five-dimensional model for electroweak physics based on a noncompact warped extra dimension of finite length, known as the soft wall scenario, where all the dynamical degrees of freedom propagate in the five-dimensional bulk. We solve the equations of motion and find the allowed spectra, showing that the mass of the lightest fermionic mode behaves as a power law of the effective four-dimensional Yukawa coupling constant, with the exponent being the corresponding fermionic five-dimensional bulk mass. Precisely this nonuniversal behavior allows us to reproduce the hierarchy between the standard model fermion masses (from neutrinos to the top quark) with nonhierarchical fermionic bulk masses.

A phase transition between small- and large-field models of inflation

We show that models of inflection point inflation exhibit a phase transition from a region in parameter space where they are of large-field type to a region where they are of small-field type. The phase transition is between a universal behavior, with respect to the initial condition, at the large-field region and non-universal behavior at the small-field region. The order parameter is the number of e-foldings. We find integer critical exponents at the transition between the two phases.

Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (model C)

We calculate the relaxational dynamical critical behavior of systems of O(n_{ parallel}) plus sign in circleO(n_{ perpendicular}) symmetry including conservation of magnetization by renormalization group theory within the minimal subtraction scheme in two-loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point, strong dynamical scaling holds, with the asymptotic dynamical critical exponent z=2varphinu-1 , where varphi is the crossover exponent and nu the exponent of the correlation length. The critical dynamics at n_{ parallel}=1 and n_{ perpendicular}=2 is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen, e.g., in the temperature dependence of the magnetic transport coefficients.

Nonuniversal Transmission Phase Lapses through a Quantum Dot: An Exact Diagonalization of the Many-Body Transport Problem

Systematic trends of nonuniversal behavior of electron-transmission phases through a quantum dot, with no phase lapse for the transition N = 1-->N = 2 and a lapse of pi for the N = 2-->N = 3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.

INTERMEDIATE VALENCE METALS

The ground state of rare earth intermediate valence (IV) metals is that of a heavy mass Fermi liquid. The transport, optical conductivity, dHvA signals, and Q-resolved neutron spectra reflect the existence of a Fermi surface with strongly renormalized masses and a hybridization gap. On the other hand, properties such as the susceptibility, specific heat, valence and spin dynamics that are dominated by the spin fluctuations, which are highly localized, can be understood qualitatively (and sometimes quantitatively) as those of a collection of non-interacting Anderson/Kondo impurities. Anomalies exist in some compounds both in the low temperature behavior and in the rate of crossover from Fermi liquid to local moment behavior which may reflect non-universal behavior of the Anderson lattice.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Marginal intermediate statistics in the excited spectra of the E ⊗ (b1 + b2) Jahn–Teller system

The long-range spectral density correlations (spectral rigidities and related spectral compressibilities) of the E ⊗ (b1 + b2) Jahn–Teller model are found strongly nonuniversal with respect to the Hamiltonian parameters and inhomogeneous with respect to the choice of a partial energy segment. However, the partial spectral rigidities exhibit common features: an anomalous linear part for small and a saturation for large . The spectral compressibilities found for the partial spectral segments and averaged over a whole relevant part of the spectrum cumulate close to a well-defined limit pertaining to the semi-Poisson statistics. This is in accordance with similar tendencies revealed in the short-range averaged statistical characteristics of this model investigated in our previous paper (Majerníková and Shpyrko 2006 Phys. Rev. E 73 057202). These features document an inhomogeneous and nonuniversal weakening of level repulsions and nonuniversality of level fluctuations on both long and short energy scales. The nonuniversality and inhomogeneity of the statistical characteristics correspond to a similar behaviour of the chaoticity parameter (a fraction of the chaotic phase space of the trajectories) found for the corresponding semiclassical Hamiltonian. We ascribe the nonuniversal and inhomogeneous nonintegrability behaviour to the changing degree of the brokening of the rotation symmetry when changing parameters of our effectively two-dimensional model. It results in a random distribution of the respective localized wavefunctions at all scales up to the size of an available state space. The multifractal behaviour of the wavefunctions is implied from the analysis of their (averaged) fractal dimensions which range up to 1.5 ± 0.1 (for ). This might imply the concept of the chaos-assisted tunnelling between the regions of reduced degree of stochasticity through regions of high degree of stochasticity. It supports the analogy with the two-dimensional Anderson model with marginal-asymptotically far metal–insulator transition. The features found allow us to classify the present model as a member of the class with a multifractal eigenfunction statistics characteristic for the spectra with weakened level repulsion similar to the Anderson model close to the metal–insulator transition.

Scaling of sound emission energy and fracture behavior of cellular solid foods

A detailed study was performed of the fracture behavior of toasted rusk rolls, a cellular solid food, at different water activities and morphologies. We find that the energies of the emitted sound pulses follow Gutenberg-Richter power laws with characteristic exponents b ~ 1.5 . The scaling exponents varied only within a range of 0.2 when the method of fracture, humidity, or morphology was changed. However, differences in b were observed, indicating nonuniversal behavior, that seems to be related to morphology and water activity. Also, power law scaling behavior was observed for the waiting time distributions with an exponent a ~ 1.9.

Universal and nonuniversal level statistics in a chaotic quantum spin chain

We study the level statistics of an interacting multiqubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasienergy level statistics show effects analogous to the ones observed in semiclassical systems due to the presence of short classical periodic orbits, while short range level statistics display perfect statistical agreement with random matrix theory. Even though our system possesses no classical limit, our results suggest existence of an important nonuniversal system specific behavior at short time scale, which clearly goes beyond finite size effects in random matrix theory.