Dependence Of Correlation Length Research Articles

Dynamical Scaling in Time dependence of Correlation Length in Non-equilibrium Critical Relaxation of Pure and Site-diluted 2D XY-model

Structural disorder in two-dimensional XY-model creates an anomalous slowing down in the process of critical relaxation. Dynamic dependences of the correlation length ξ(t) show slow growth with an “effective” dynamical critical exponent z > 2. For a pure system, it has been shown that a detailed consideration of the vortex dynamics leads to deviations from the known dependence ξ(t) ∼ (t/ln t)1/2.

2D scaling behavior of nanotextured GaN surfaces: A case study of hillocked and terraced surfaces

The 2D scaling properties of GaN surfaces have been studied by means of the 2D height–height correlation function (HHCF). The GaN layers under investigation presented exemplar morphologies, generated by distinct growth methods: a molecular beam epitaxy (MBE) grown surface decorated by hillocks and a metal organic vapor phase epitaxy (MOVPE) grown surface with terraced structure. The 2D statistical analysis of these surfaces has allowed assessing quantitatively the degree of morphological variability along all the different directions across each surface, their corresponding roughness exponents and correlation lengths. A scaling anisotropy as well as correlation length anisotropy has been detected for both hillocked and terraced surfaces. Especially, a marked dependence of correlation length from the direction across the terraced surface has been observed. Additionally, the terraced surfaces showed the lower root mean square (RMS) roughness value and at the same time, the lower roughness exponent value. This could appear as a contradiction, given that a low RMS value is associated to a smooth surface, and usually the roughness exponent is interpreted as a “measure” of the smoothness of the surface, the smoother the surface, the higher (approaching the unity) is the roughness exponent. Our case study is an experimental demonstration in which the roughness exponent should be, more appropriately, interpreted as a quantification of how the roughness changes with length scale.

Thickness dependence and dimensionality effects on charge and magnetic orderings in La1/3Sr2/3FeO3 thin films

We investigate the thickness effects on charge and magnetic orderings in Fe perovskite oxide La1/3Sr2/3FeO3/SrTiO3 thin films by hard x-ray and resonant soft x-ray scattering (RSXS) with changing thin film thickness systematically. We found that the correlation lengths of the magnetic ordering along the in-plane and out-of-plane directions are comparable and proportional to the thickness, and shows stronger thickness dependence than those of charge orderg. %the thickness dependence of correlation length of charge ordering is smaller than that of magnetic orderings. The magnetic ordered states disappear when the correlation length of magnetic ordering decreases to that of charge ordering through the intrinsic thickness effects. Surface sensitive grazing-incident RSXS revealed that the orderings exist even in the surface region, which indicates that the observed orderings is not affected by surface effect like oxygen vacancies. Critical thickness is in 5-15 nm, which corresponds to 4-11 antiferromagnetic ordering period. This critical value seems to be common to other ferromagnetic oxide thin films.

Thickness effect on the structure, grain size, and local piezoresponse of self-polarized lead lanthanum zirconate titanate thin films

Polycrystalline lanthanum lead zirconate titanate (PLZT) thin films were deposited on Pt/TiO2/SiO2/Si substrates to study the effects of the thickness and grain size on their structural and piezoresponse properties at nanoscale. Thinner PLZT films show a slight (100)-orientation tendency that tends to random orientation for the thicker film, while microstrain and crystallite size increases almost linearly with increasing thickness. Piezoresponse force microscopy and autocorrelation function technique were used to demonstrate the existence of local self-polarization effect and to study the thickness dependence of correlation length. The obtained results ruled out the bulk mechanisms and suggest that Schottky barriers near the film-substrate are likely responsible for a build-in electric field in the films. Larger correlation length evidence that this build-in field increases the number of coexisting polarization directions in larger grains leading to an alignment of macrodomains in thinner films.

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpi\'{n}ski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\'{n}ski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi\'{n}ski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.

Beam Energy Dependence of Hanbury-Brown-Twiss Radii from a Blast-Wave Model

The beam energy dependence of correlation lengths (the Hanbury-Brown-Twiss radii) is calculated by using a blast-wave model and the results are comparable with those from RHIC-STAR beam energy scan data as well as the LHC-ALICE measurements. A set of parameters for the blast-wave model as a function of beam energy under study are obtained by fit to the HBT radii at each energy point. The transverse momentum dependence of HBT radii is presented with the extracted parameters for Au+Au collision at sNN = 200 GeV and for Pb+Pb collisions at 2.76 TeV. From our study one can learn that particle emission duration cannot be ignored while calculating the HBT radii with the same parameters. And tuning kinetic freeze-out temperature in a range will result in system lifetime changing in the reverse direction as it is found in RHIC-STAR experiment measurements.

Viscosities and their correlations with structures of Cu–Ag melts**Project supported by the Science and Technology Development Program of Shandong Province, China (Grant No. 2011YD03099) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014EL001).

The viscosities of a series of Cu–Ag melts in a temperature range from 1473 K to nearly liquid temperatures are measured by using an oscillating viscometer. At the same temperature, the value of viscosity increases first with silver content increasing, and reaches a maximum value at the eutectic component Cu40Ag60, then decreases. All the temperature dependences of the viscosities of Cu–Ag melts conform with the Arrhenius equation. The parameters of correlation length D of the studied Cu–Ag melts are calculated according to the experimental results of x-ray diffraction. The temperature dependence of correlation length D shows an exponential decay function, which is similar to the Arrhenius equation. Based on the values of viscosities and correlation length D, a direct correlation between viscosity and liquid structure is found for the investigated Cu–Ag melts through comparative analysis.

Variability of interconnected wind plants: correlation length and its dependence on variability time scale

The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. But how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer ‘how far is far enough,’ we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of five-minute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25–2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high-pass filter time constants shorter than about τ = 38 h, all datasets exhibit a correlation length that falls at least as fast as . Since the inter-site separation needed for statistical independence falls for shorter time scales, higher-rate fluctuations can be effectively smoothed by aggregating wind plants over areas smaller than otherwise estimated.

Evolution of lateral ordering in symmetric block copolymer thin films upon rapid thermal processing

This work reports experimental findings about the evolution of lateral ordering of lamellar microdomains in symmetric PS-b-PMMA thin films on featureless substrates. Phase separation and microdomain evolution are explored in a rather wide range of temperatures (190–340 °C) using a rapid thermal processing (RTP) system. The maximum processing temperature that enables the ordering of block copolymers without introducing any significant degradation of macromolecules is identified. The reported results clearly indicate that the range of accessible temperatures in the processing of these self-assembling materials is mainly limited by the thermal instability of the grafted random copolymer layer, which starts to degrade at T > 300 °C, inducing detachment of the block copolymer thin film. For T ⩽ 290 °C, clear dependence of correlation length (ξ) values on temperature is observed. The highest level of lateral order achievable in the current system in a quasi-equilibrium condition was obtained at the upper processing temperature limit after an annealing time as short as 60 s.

Study on filler content dependence of the onset of positive temperature coefficient (PTC) effect of electrical resistivity for UHMWPE/LDPE/CF composites based on their DC and AC electrical behaviors

Composites of carbon fibers (CF) filled with ultrahigh molecule weight polyethylene/low density polyethylene blend matrix (UHMWPE/LDPE) were prepared by kneading method. The positive temperature coefficient (PTC) effect of electrical resistivity of UHMWPE/LDPE/CF composites was investigated by direct current (DC) and alternating current (AC) measurements over the frequency range of 100–106.5 Hz from 30 to 150 °C. The onsets of PTC effect were found to be strongly depended upon the CF content even the melting behaviors were almost same for all composites. To interpret this phenomenon, a master curve of temperature–frequency–resistivity superposition was constructed for composites with different CF contents based on the AC resistivity. The CF content dependence of correlation length was related to the onset of PTC effect. The transitions of conductor–insulator were studied quantitatively by complex planes of AC impedance, and the calculated capacitances and resistances showed a similar PTC effect under DC. Based on the analysis of AC capacitance, the average distances between CFs were calculated using a plane capacitance model which varied with CF concentration and temperature, and the tendency was consistent to the PTC effect.

Dynamics and correlation length scales of a glass-forming liquid in quiescent and sheared conditions

We numerically study dynamics and correlation length scales of a colloidal liquid in both quiescent and sheared conditions to further understand the origin of slow dynamics and dynamic heterogeneity in glass-forming systems. The simulation is performed in a weakly frustrated two-dimensional liquid, where locally preferred order is allowed to develop with increasing density. The four-point density correlations and bond-orientation correlations, which have been frequently used to capture dynamic and static length scales ξ in a quiescent condition, can be readily extended to a system under steady shear in this case. In the absence of shear, we confirmed the previous findings that the dynamic slowing down accompanies the development of dynamic heterogeneity. The dynamic and static length scales increase with α-relaxation time τα as a power law , with μ > 0. In the presence of shear, both viscosity and τα have power-law dependences on shear rate in the marked shear-thinning regime. However, the dependence of correlation lengths cannot be described by power laws in the same regime. Furthermore, the relation between length scales and dynamics holds for not too strong shear where thermal fluctuations and external forces are both important in determining the properties of dense liquids. Thus, our results demonstrate a link between slow dynamics and structure in glass-forming liquids even under nonequilibrium conditions.

Universal properties of frustrated spin systems: [formula omitted]-expansion and renormalization group approaches

We consider a quantum two-dimensional O ( N ) ⊗ O ( 2 ) / O ( N − 2 ) ⊗ O ( 2 ) diag nonlinear sigma model for frustrated spin systems and formulate its 1 / N -expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1 / N -expansion and 2 + ε renormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region ρ in < ρ out , χ in < χ out of the symmetry broken ground state ( ρ in , out and χ in , out are the in- and out-of-plane spin stiffnesses and susceptibilities) the mass M μ of the vector field can be arbitrarily small, and physical properties at finite temperatures are universal functions of ρ in , out , χ in , out , and temperature T. For small enough M μ these properties show a crossover from low- to high temperature regime at T ∼ M μ . In the region ρ in > ρ out or χ in > χ out finite-temperature properties are universal functions only at sufficiently large M μ . The high-energy behaviour in the latter region is similar to the Landau-pole dependence of the physical charge e on the momentum scale in quantum electrodynamics, with mass M μ playing a role of e −1 . The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.

The correlation length of 3D Ising systems in the presence of an external field

The explicit dependence of correlation length as function of temperature and external field is found for the Ising model on a simple cubic lattice near the phase transition point. , where and h c are the renormalized values of the external field h and reduced temperature τ. The critical amplitude ξ0 is proportional to the lattice constant through the coefficient, which is determined by the parameter of the interaction potential. The size of the critical region is established by the temperature and field. It is shown that the essential increasing of the system correlation length takes place at () with h→0 and at h′<h* (, h′=βh) with τ→0.

Velocity correlations in dense gravity-driven granular chute flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time Deltat used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size, and grain stiffness and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.

A sigma-model approach to glassy dynamics

In this contribution we review recent progress in understanding fluctuations in the aging process of macroscopic systems, and we propose further tests of these ideas. We discuss how the emergence of a symmetry in aging systems, global timereparametrization invariance, could be responsible for the observed ‘universal’ behavior of local and mesoscopic non-equilibrium fluctuations. We discuss (i) the two-time scaling and functional form of the distribution of local correlations and responses; (ii) the scaling of multi-time correlations and susceptibilities; (iii) how the above can be derived from a random surface effective action; (iv) the behavior of a diverging two-time dependent correlation length; (v) how these ideas apply to off-lattice particle systems.

Pseudogap and Spin Fluctuations in the Normal State of the Electron-Doped Cuprates

We present reliable many-body calculations for the t-t(')-t('')-U Hubbard model that explain in detail the results of recent angle-resolved photoemission experiments on electron-doped high-temperature superconductors. The origin of the pseudogap is traced to two-dimensional antiferromagnetic spin fluctuations whose calculated temperature-dependent correlation length also agrees with recent neutron scattering measurements. We make specific predictions for photoemission, for neutron scattering, and for the phase diagram.

External field dependence of the correlation lengths in the three-dimensional O(4) model

We investigate numerically the transverse and longitudinal correlation lengths of the three-dimensional O(4) model as a function of the external field H. In the low-temperature phase we verify explicitly the H^{-1/2}-dependence of the transverse correlation length, which is expected due to the Goldstone modes of the model. On the critical line we find the universal amplitude ratio xi^c_T / xi^c_L = 1.99(1). From our data we derive the universal scaling function for the transverse correlation length. The H-dependencies of the correlation lengths in the high temperature phase are discussed and shown to be in accord with the scaling functions.

Spatially heterogeneous ages in glassy systems

We construct a framework for the study of fluctuations in the nonequilibrium relaxation of glassy systems with and without quenched disorder. We study two types of two-time local correlators with the aim of characterizing the heterogeneous evolution: in one case we average the local correlators over histories of the thermal noise, in the other case we simply coarse-grain the local correlators. We explain why the former describe the fingerprint of quenched disorder when it exists, while the latter are linked to noise-induced mesoscopic fluctuations. We predict constraints on the pdfs of the fluctuations of the coarse-grained quantities. We show that locally defined correlations and responses are connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. We argue that large-size heterogeneities in the age of the system survive in the long-time limit. The invariance of the theory under reparametrizations of time underlies these results. We relate the pdfs of local coarse-grained quantities and the theory of dynamic random manifolds. We define a two-time dependent correlation length from the spatial decay of the fluctuations in the two-time local functions. We present numerical tests performed on disordered spin models in finite and infinite dimensions. Finally, we explain how these ideas can be applied to the analysis of the dynamics of other glassy systems that can be either spin models without disorder or atomic and molecular glassy systems.

Effect of pick-up ions on the magnetic field correlation length: Implications for solar modulation of galactic cosmic rays

In this study the solar modulation of cosmic rays is modeled by direct numerical simulation of Parker's transport equation. We use our ab initio modulation model where the diffusion tensor is specified by particle scattering theory based on observed properties of the turbulence, and the spatial variation is determined by turbulence transport models that specify how turbulence properties vary throughout the heliosphere. We discuss the effect of pick-up ions on the spatial dependence of the magnetic field correlation length which is not well understood. If the effect is negligible, turbulence models suggest that the correlation length should increase almost monotonically with radial distance. If not, it should at some point (determined by the size of the ionization cavity) start to decrease. We model such a two-stage behavior by assuming two power laws for the radial dependence of the correlation length. We show that varying the position of the breakpoint between the two power laws by as little as 10 AU has large effects on the radial intensity profiles and provides better agreement with observation than when a single power law is used (Parhi et al. 2002, 2003).

Theory for disordered phase in Heisenberg and non-Heisenberg two-dimensional S=1 ferromagnets

We apply a modification of self-consistent spin-wave theory to investigation of two-dimensional S=1 isotropic Heisenberg and non-Heisenberg ferromagnets at nonzero temperatures. We use Hubbard operators method and bosonization technique. We calculated chemical potential and found dependence of correlation length on temperature. Specific heat has Schottky-type peak and decreases at high temperatures. Disordered phase in non-Heisenberg ferromagnet is also studied. The results for such a model differ from those of Heisenberg one.