Dynamic Scaling Theory Research Articles

Percolation phase transition, self-organization processes and thermal conductivity in PbSe1-xTex semiconductor solid solutions at small Te concentration

ABSTRACT The isotherms of the lattice thermal conductivity λ L for the PbSe1-xTex semiconductor solid solutions (х = 0–0.045) were obtained in the temperature range T = (200–600) K. The λ L(x) dependences exhibit a general trend to a decrease in λ L with increasing x, but the peaks are observed near x = 0.007, 0.015 and 0.0025 indicating the presence of phase transformations. We associated the first peak with a percolation-type phase transition to the impurity continuum and estimated the critical index for λ L within the framework of dynamic scaling theory. The second and third peaks were attributed to the self-organization processes in the PbSe1-xTex after the percolation threshold reaching. The effective cross-sections σ s for phonon scattering by impurity (Te) atoms were determined experimentally and calculated theoretically using the Klemens theory. The data obtained are another confirmation of our assumption about the presence of such percolation-type phase transition in any solid solution.

Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions

The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time-concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions.

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξs) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient Dc of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), Dc = kBT/6πηξs, where ξs is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient Dc(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

Secondary electron emission behavior of nanostructured fluorocarbon film

Based on the theoretical analysis of secondary electron emission (SEE) behavior of semiconductor and insulator, this paper numerically calculates electron affinity (EA) and energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of fluorocarbon (FC) films with the variation of fluorine to carbon (F/C) ratio. As fluorine element exhibits strong electronegativity, the LUMO energy decreases and the EA increases with the incremental content of fluorine. Increasing F/C ratio contributes to stronger electron capture capacity. SEE behavior is mainly affected by the chemical compositions and island-like nanostructure of FC films. Based on the dynamic scaling theory, the growth process is divided into two stages, in which roughening and smoothing effects play the dominant role, respectively. Growth index of the two stages are 0.57±0.01 and 0.10±0.01. Prolonging sputtering time contributes to higher film thickness, bigger surface roughness and larger F/C ratio. Experimental results confirm that secondary electron emission yield (SEY) decreases from 3.02 to 1.60, as film thickness increases from 19 to 113 nm. After 7 days and 60 days aging, the highest incremental δmax is 3.68% and the largest reduced E1 is 11.11%. The SEE behavior of FC film is relatively stable in the atmosphere.

Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time

Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We explicitly show the deconfinement dynamic process and identify that it is the spinon confinement length, rather than the usual correlation length, that increases proportionally to the time. Moreover, we find that, in the relaxation process, the order parameters of the Néel and the valence-bond-solid orders can be controlled by different length scales, although they satisfy the same equilibrium scaling forms. A dual dynamic scaling theory is then proposed. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems. Possible realizations in foreseeable quantum computers are also discussed.

Analysis of methods for calculating the thermal conductivity of new liquid hydrofluorochlorine derivatives of olefins on the saturation line

We consider various correlations to calculate thermal conductivity of the refrigerants in the state of a saturated liquid. An analysis of these dependencies was carried out using the example of refrigerants R1234yf, R1224yd(Z), R1233zd(E), R1234ze(E), R1243zf, R1336mzz(E), R1336mzz(Z), R365mfc, and R245fa. A modified linear dependence I for λsat = λsat(T) is proposed. Statistical characteristics for the model I are given, in particular, the average absolute deviation is calculated AADI = 3,37%. It is shown that, taking into account the nonlinear nature of the behavior of thermal conductivity λsat = λsat(T) on temperature, model II, makes it possible to increase the accuracy of calculations using the model II: AAD = 2,39%. In contrast to the known correlation dependences, within the framework of the model II, in accordance with the dynamic scale theory, the passage to the limit λsat(T→Tc)~τ-χ is performed in the vicinity of the critical point, where τ = (Tc – T)/Tc, Tc is the critical temperature, χ = 0,608 is the critical index. The results are discussed.

Deposition-rate dependent kinetic roughening for nanoscale sputter-deposited Cu films on Si surface

This work presents an experimental study on the kinetic roughening for nanoscale-thick sputter-deposited Cu films on Si surface. In particular, the Cu films were deposited by using two different deposition rates and their Root-Mean-Square surface roughness was quantified by means of atomic force microscopy measurements. The results of these analyses are discussed on the basis of the dynamic scaling theory and, hence, evaluating the steady growth roughness exponent α and the dynamic growth roughness exponent β. We find a value for α = 0.89 ± 0.07 independent on the Cu deposition rate, while a value of β = 0.23 ± 0.03 at the lower Cu deposition rate (1.7 nm/min) and a value of β = 0.64 ± 0.05 at the higher Cu deposition rate (7.0 nm/min). At the lower deposition rate, the combined values of α = 0.89 ± 0.07 and β = 0.23 ± 0.03 suggest a growth process for the Cu film in thermodynamic equilibrium and dominated by surface diffusion. On the other hand, the combined values of α = 0.89 ± 0.07 and β = 0.64 ± 0.05 suggest a growth process again dominated by surface diffusion however with the occurrence of growing instabilities.

Self-organized criticality in neural networks from activity-based rewiring.

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis, which suggests that neural systems reach such a state by self-organizing toward the critical point of a dynamical phase transition. Here, we study a minimal neural network model that exhibits self-organized criticality in the presence of stochastic noise using a rewiring rule which only utilizes local information. For network evolution, incoming links are added to a node or deleted, depending on the node's average activity. Based on this rewiring-rule only, the network evolves toward a critical state, showing typical power-law-distributed avalanche statistics. The observed exponents are in accord with criticality as predicted by dynamical scaling theory, as well as with the observed exponents of neural avalanches. The critical state of the model is reached autonomously without the need for parameter tuning, is independent of initial conditions, is robust under stochastic noise, and independent of details of the implementation as different variants of the model indicate. We argue that this supports the hypothesis that real neural systems may utilize such a mechanism to self-organize toward criticality, especially during early developmental stages.

Transported properties and low-temperature magnetic behaviors of Ti x Cr1− x O2 films

Electronic transport and magnetic properties of Ti x Cr1−x O2 epitaxial films with low Ti concentrations have been studied. Compared with pure CrO2 film, Ti-doped films exhibit a significant increase of resistivity and the magnetoresistance at low temperature is more difficult to saturate even under an external field of 5 Tesla. The DC magnetization and AC susceptibility measurements suggest that a cluster glass freezing behavior occurs at low temperature in Ti-doped films. After analyzing the AC susceptibility using dynamic scaling theory, we have obtained the cluster-glass transition temperature T G = 97.8 K, the dynamic exponent zv = 12.37, and the characteristic timescale τ 0 = 10−16, which lies in the range of conventional cluster glass systems.

Temperature scaling in nonequilibrium relaxation in three-dimensional Heisenberg model in the Swendsen-Wang and Metropolis algorithms.

Recently the present authors proposed the nonequilibrium-to-equilibrium scaling (NE-ES) scheme for the critical Monte Carlo relaxation process [Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)10.7566/JPSJ.83.113001], which scales relaxation data in the whole simulation-time regions regardless of functional forms, namely, both for the stretched-exponential critical relaxation in cluster algorithms and for the power-law critical relaxation in local-update algorithms. In the present study, we generalize this scheme to off-critical relaxation process and scale relaxation data for various temperatures in the whole simulation-time regions. This proposal of the off-critical scaling in cluster algorithms cannot be described by the dynamical finite-size scaling theory based on the power-law critical relaxation. As an example, we investigate the three-dimensional classical Heisenberg model previously analyzed with the NE-ES [Nonomura and Tomita, Phys. Rev. E 93, 012101 (2016)10.1103/PhysRevE.93.012101] in the Swendsen-Wang and Metropolis algorithms.

Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases.

We address the out-of-equilibrium dynamics of a many-body system when one of its Hamiltonian parameters is driven across a first-order quantum transition (FOQT). In particular, we consider systems subject to boundary conditions favoring one of the two phases separated by the FOQT. These issues are investigated within the paradigmatic one-dimensional quantum Ising model, at the FOQTs driven by the longitudinal magnetic field h, with boundary conditions that favor the same magnetized phase (EFBC) or opposite magnetized phases (OFBC). We study the dynamic behavior for an instantaneous quench and for a protocol in which h is slowly varied across the FOQT. We develop a dynamic finite-size scaling theory for both EFBC and OFBC, which displays some remarkable differences with respect to the case of neutral boundary conditions. The corresponding relevant timescale shows a qualitative different size dependence in the two cases: it increases exponentially with the size in the case of EFBC, and as a power of the size in the case of OFBC.

Berezinskii–Kosterlitz–Thouless transition in an Al superconducting nanofilm grown on GaAs by molecular beam epitaxy

We have performed extensive transport experiments on a 4 nm thick aluminum (Al) superconducting film grown on a GaAs substrate by molecular beam epitaxy (MBE). Nonlinear current–voltage (I–V) measurements on such a MBE-grown superconducting nanofilm show that V ∼ I3, which is evidence for the Berezinskii–Kosterlitz–Thouless (BKT) transition, both in the low-voltage (TBKT ≈ 1.97 K) and high-voltage regions (TBKT ≈ 2.17 K). In order to further study the two regions where the I–V curves are BKT-like, our experimental data are fitted to the temperature-induced vortices/antivortices unbinding model as well as the dynamical scaling theory. It is found that the transition temperature obtained in the high-voltage region is the correct TBKT as confirmed by fitting the data to the aforementioned models. Our experimental results unequivocally show that I–V measurements alone may not allow one to determine TBKT for superconducting transition. Therefore, one should try to fit one’s results to the temperature-induced vortices/antivortices unbinding model and the dynamical scaling theory to accurately determine TBKT in a two-dimensional superconductor.

Evolution of Morphology in the Process of Growth of Island Poly(p-xylylene) Films Obtained by Vapor Deposition Polymerization

Using atomic force microscopy, the evolution of the morphology of island poly(p-xylene) films formed on silicon substrates by vapor deposition polymerization at two deposition temperatures of +23 and 0°C and a fixed monomer flow is studied. The dependences of the surface coverage, the effective thickness of the island coating, and the density and average size of the polymer islands on the deposition time are investigated. Within the framework of the dynamic scaling theory, the size distribution of islands and the size distribution of their capture zones are analyzed. It is shown that the observed features of the evolution of the morphology of island poly(p-xylylene) films cannot be fully described in the framework of classical models based on diffusion-limited aggregation. However, they can be explained by the reversibility of aggregation, which is a specific feature of the polymeric nature of the island coatings being formed.

Scaling behavior of Ising systems at first-order transitions

We investigate how the scaling behavior of finite systems at magnetic first-order transitions (FOTs) with relaxational dynamics changes in correspondence of various boundary conditions. As a theoretical laboratory, we consider the two-dimensional Ising model in the low-temperature phase. When the boundary conditions do not favor any specific phase of the system, we show that a dynamic finite-size scaling (DFSS) theory can be developed to describe the dynamic behavior in the coexistence region, where different phases coexist. When the boundary conditions at two opposite sides of the system generate a planar interface separating the phases, we show that the autocorrelation times are characterized by a power-law behavior, related to the dynamics enforced by the interface. Numerical results for a purely relaxational dynamics confirm the general picture.

Dipolar interactions in Fe: A study with the neutron Larmor precession technique MIEZE in a longitudinal field configuration

While the influence of dipolar interactions on the spin-wave dispersion in ferromagnets with localized magnetic moments has been studied in detail, similar studies in itinerant electron systems are rather scarce due to experimental difficulties. Using the newly developed neutron Larmor precession technique MIEZE in a longitudinal field configuration, we succeeded to map out the spin-wave dispersion in Fe at small momentum $q$ and energy transfers $E$. The results demonstrate an excellent agreement of the magnon dispersion with the Holstein-Primakoff theory, which takes the dipolar interactions into account. At larger $q$, the data is in agreement with previous investigations by Collins et al., Phys. Rev. 179, 417 (1969). The $q$ dependence of the linewidth of the magnons is proportional to ${q}^{2.5}$ in agreement with dynamical scaling theory. The critical exponent for the stiffness, $\ensuremath{\mu}=0.35\ifmmode\pm\else\textpm\fi{}0.01$, agrees with field theory. The spin dynamics in Fe is now explored by neutron scattering over an energy range $15\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{eV}\phantom{\rule{4pt}{0ex}}l{E}_{\mathrm{sw}}l120\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, i.e., over about four orders of magnitude in energy.

Scaling of decoherence and energy flow in interacting quantum spin systems

We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity of a quantum first-order or continuous phase transition. Although the approach is quite general, we consider d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields, as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchanges among the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing the system size.

The behavior of sound absorption coefficient for binary mixture nitroethane-isooctane above critical temperature and concentration

The temperature dependence of the sound absorption coefficient at critical composition and above critical temperature Tc for the binary mixture nitroethane-isooctane at 5, 7, 10, 15, 21, and 25 MHz frequencies (f) is investigated. The frequency dependence of the absorption coefficient (α) for the same critical binary mixture at different temperatures above critical temperature is studied. In addition, the linear relation of the sound absorption coefficient at critical point (αc)/f2 versus f−1.06 showed an excellent agreement with the dynamic scaling theory of Ferrell and Bhattacharjee, Physical Review A 31, 1788 (1985). The experimental values of (αf−2αcf−2) for nitroethane-isooctane binary mixture are plotted as a function of reduced frequency Ω and it showed a good agreement with the theoretical scaling function F(Ω).

Anomalies of the Sound Absorption Coefficient for Binary Solutions with a Critical Stratification Temperature

The results of the analysis of experimental data concerning the sound absorption in the nitro-methane–n-pentanol and nitrobenzene-n-hexane solutions obtained in a wide frequency interval of 5–2800 MHz and measured along the isotherms and isoconcentrates, including their critical values, are presented. The detected anomalous dependences of the sound absorption coefficient were found to obey the laws of the dynamic scaling theory only in the fluctuation region of the problem parameters, wтfl ≫ 1. The sound frequency growth (f ≥ 110 MHz) in the examined frequency interval, as well as moving away from the critical temperature and concentration values, is proved to transit the system from the critical region into the crossover, wтfl ∼ 1, or even hydrodynamic, wтfl ≪ 1, one.

Dynamic finite-size scaling after a quench at quantum transitions.

We present a general dynamic finite-size scaling theory for the quantum dynamics after an abrupt quench, at both continuous and first-order quantum transitions. For continuous transitions, the scaling laws are naturally ruled by the critical exponents and the renormalization-group dimension of the perturbation at the transition. In the case of first-order transitions, it is possible to recover a universal scaling behavior, which is controlled by the size behavior of the energy gap between the lowest-energy levels. We discuss these findings in the framework of the paradigmatic quantum Ising ring, and support the dynamic scaling laws by numerical evidence.

Evidence of low temperature spin glass transition in bixbyite type FeMnO3

We report the solution combustion synthesis of FeMnO3 as well as its detailed structural and magnetic characterizations. The X-ray and electron diffraction studies were utilized for structural characterization. It crystallizes in cubic Ia3 space group with bixbyite structure having cell parameter a = 9.413(4) Å. It is observed that FeMnO3 lacks long range ordering and shows spin glass behaviour with a freezing temperature Tg ∼ 33 K. This result is in contradiction with the earlier reports of long range antiferromagnetic and ferrimagnetic ordering. The prevalence of spin glass state has been explained with the most relevant dynamic scaling theory giving the glass transition, critical exponent and characteristic time, respectively, Tg = 33 ± 0.2 K, zν = 5.7 ± 0.5 and τ0 ∼ 10−12 s. The evolution of spin glass state can be ascribed to the structural genesis, where the competing antiferromagnetic and ferromagnetic interaction as well as cationic disordering results in magnetic frustration.