Smectic vortex phase in optimally doped YBa2Cu3O7 thin films

Angular dependent resistivity measurements of optimally doped YBa2Cu3O7 films in fields H pulsed to 50 T are presented. Up to the highest H, the vortex melting field Hm increases and vortex motion is reduced for H aligned with the correlated pinning centers along the main crystalline axes, otherwise 3D anisotropic scaling describes the vortex dynamics. For H parallel ab, the rapid increase in Hm at low temperatures and a critical exponent analysis near Hm confirm the presence of the liquid-crystalline smectic phase predicted for layered superconductors.     

Critical phenomena in a disc-percolation model and their application to relativistic heavy ion collisions

By studying the critical phenomena in continuum-percolation of discs, we find a new approach to locate the critical point, i.e.using the inflection point of P_∞ as an evaluation of the percolation threshold.The susceptibility, defined as the derivative of P_∞, possesses a finite-size scaling property, where the scaling exponent is the reciprocal of ν, the critical exponent of the correlation length.A possible application of this approach to the study of the critical phenomena in relativistic heavy ion collisions is discussed.The critical point for deconfinement can be extracted by the inflection point of P_(QGP)-the probability for the event with QGP formation.The finite-size scaling of its derivative can give the critical exponent ν, which is a rare case that can provide an experimental measure of a critical exponent in heavy ion collisions.     

Reduced fidelity, entanglement and quantum phase transition in the one-dimensional bond-alternating S = 1 Heisenberg chain

By using the method of density-matrix renormalization group, the reduced fidelity and entanglement in the one-dimensional bond-alternating S = 1 Heisenberg chain are investigated. The results demonstrate that the quantum phase transition from the Haldane phase to the dimer phase can be characterized by the reduced fidelity and the first derivation of the entanglement entropy. Through the finite-size scaling, the critical point and the critical exponent of the correlation length are obtained accurately.     

Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.     

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation of the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b ≈ 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin-wave excitations renders the dephasing length L(?) ? b in the range of sheet resistances considered, so that the effective dimension is d = 3. The conductivity data at different stages of disorder obey a fractional power-law temperature dependence and collapse onto two scaling curves for the metallic and insulating regimes, indicating an asymmetric metal-insulator transition with two distinctly different critical exponents; the best fit is obtained for a dynamical exponent z ≈ 2.5 and a correlation (localization) length critical exponent ν- ≈ 1.4 (ν+ ≈ 0.8) on the metallic (insulating) side.     

A random field model for anomalous diffusion in heterogeneous porous media

Heterogeneity, as it occurs in porous media, is characterized in terms of a scaling exponent, or fractal dimension. A feature of primary interest for two-phase flow is the mixing length. This paper determines the relation between the scaling exponent for the heterogeneity and the scaling exponent which governs the mixing length. The analysis assumes a linear transport equation and uses random fields first in the characterization of the heterogeneity and second in the solution of the flow problem, in order to determine the mixing exponents. The scaling behavior changes from long-length-scale dominated to short-length-scale dominated at a critical value of the scaling exponent of the rock heterogeneity. The long-length-scale-dominated diffusion is anomalous.     

Anderson transition in two-dimensional systems with spin-orbit coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent nu for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyze the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent nu=2.73+/-0.02.     

Scaling exponents for fracture surfaces in homogeneous glass and glassy ceramics

We investigate the scaling properties of postmortem fracture surfaces in silica glass and glassy ceramics. In both cases, the 2D height-height correlation function is found to obey Family-Viseck scaling properties, but with two sets of critical exponents, in particular, a roughness exponent zeta approximately 0.75 in homogeneous glass and zeta approximately 0.4 in glassy ceramics. The ranges of length scales over which these two scalings are observed are shown to be below and above the size of the process zone, respectively. A model derived from linear elastic fracture mechanics in the quasistatic approximation succeeds to reproduce the scaling exponents observed in glassy ceramics. The critical exponents observed in homogeneous glass are conjectured to reflect the damage screening occurring for length scales below the size of the process zone.     

Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.     

Nonlinear electric field effects at a continuous mott-hubbard transition

We characterize the non-Ohmic portion of the conductivity at temperatures T<1 K in the highly correlated transition metal chalcogenide Ni(S,Se)(2). Pressure tuning of the T = 0 metal-insulator transition reveals the influence of the quantum critical point and permits a direct determination of the dynamical critical exponent z = 2.7(+0.3)(-0.4). Within the framework of finite temperature scaling, we find that the spatial correlation length exponent nu and the conductivity exponent &mgr; differ.     

Critical properties of the three-dimensional frustrated Ising model on a cubic lattice

The critical properties of the three-dimensional fully frustrated Ising model on a cubic lattice are investigated by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length), as well as the Fisher exponent η, are calculated in the framework of the finite-size scaling theory. It is demonstrated that the three-dimensional frustrated Ising model on a cubic lattice forms a new universality class of the critical behavior.     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Aperiodic extended surface perturbations in the Ising model

We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power of the distance l from the free surface with an oscillating amplitude where follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean amplitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent , the wandering exponent which governs the fluctuation of the sequence and the bulk correlation length exponent . Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the -plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed. Received 1 December 1998     

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. We report a finite-size scaling analysis using both the traditional power-law corrections to the scaling function and the inverse logarithmic ones, which provided a more stable fit resulting in the localization length critical index ν = 2.616 ± 0.014. We observe an increase of the critical exponent ν with the system size, which is possibly the origin of discrepancies with early results obtained for smaller systems.     

Vortex glass transition in a frustrated 3D XY model with disorder

The anisotropic frustrated three-dimensional (3D) XY model with disorder in the coupling constants is simulated as a model of a point disordered superconductor in an applied magnetic field. A finite size scaling analysis of the helicity modulus gives strong evidence for a finite temperature transition with isotropic scaling and the correlation length exponent nu=1.5+/-0.3, consistent with 3D gauge glass universality.     

Dynamic scaling approach to glass formation

Experimental data for the temperature dependence of relaxation times are used to argue that the dynamic scaling form, with relaxation time diverging at the critical temperature T(c) as (T-T(c))(-nuz), is superior to the classical Vogel form. This observation leads us to propose that glass formation can be described by a simple mean-field limit of a phase transition. The order parameter is the fraction of all space that has sufficient free volume to allow substantial motion, and grows logarithmically above T(c). Diffusion of this free volume creates random walk clusters that have cooperatively rearranged. We show that the distribution of cooperatively moving clusters must have a Fisher exponent tau=2. Dynamic scaling predicts a power law for the relaxation modulus G(t) approximately t(-2/z), where z is the dynamic critical exponent relating the relaxation time of a cluster to its size. Andrade creep, universally observed for all glass-forming materials, suggests z=6. Experimental data on the temperature dependence of viscosity and relaxation time of glass-forming liquids suggest that the exponent nu describing the correlation length divergence in this simple scaling picture is not always universal. Polymers appear to universally have nuz=9 (making nu=3 / 2). However, other glass-formers have unphysically large values of nuz, suggesting that the availability of free volume is a necessary, but not sufficient, condition for motion in these liquids. Such considerations lead us to assert that nuz=9 is in fact universal for all glass- forming liquids, but an energetic barrier to motion must also be overcome for strong glasses.     

Critical scaling of shear viscosity at the jamming transition

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity eta is computed as a function of particle volume density rho and applied shear stress sigma, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable sigma/|rho(c)-rho|(Delta), where rho(c) is the critical density at sigma=0 ("point J"), and Delta is the crossover scaling critical exponent. We define a correlation length xi from velocity correlations in the driven steady state and show that it diverges at point J. Our results support the assertion that jamming is a true second-order critical phenomenon.     

东亚区域大气长程相关性

运用去趋势涨落分析方法分别研究NCEP/NCAR再分析资料中的高度场和温度场,揭示了东亚区域高度场和温度场的标度指数分布特征.结果表明高度场和温度场都具有长程相关性,且二者空间分布特征总体匹配.对同一层格点资料而言,低纬度地区标度指数较大,长程相关性较好;中高纬度地区标度指数较小,长程相关性较差,呈现比较明显的纬向分布特征.不同层格点资料的标度指数分布有所区别,具体表现为高度场资料随层数的增加,其平均标度指数值呈增长趋势且纬向分布特征更为明显;在高度场中下层青藏高原地区标度指数明显大于同纬度其他区域.温度场资料随层数的增加平均标度指数先减小再增大,也具有一定的纬向分布特征.总体而言,高度场长程相关性的标度指数值要高于温度场.分季节研究表明,高度场和温度场也具有较好的长程相关性,冬季标度指数高于其他季节,为利用冬季信息制作夏季汛期预报提供了一定的理论依据. 关键词： 高度场 温度场 长程相关性 去趋势涨落分析     

Cascade of quantum phase transitions in tunnel-coupled edge states

We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields B(c) is a function of a single scaling argument /B-B(c)/T(-kappa), where the exponent kappa=0.42. This puzzling resemblance to a quantum Hall-insulator transition points to the importance of interedge correlation between the coupled edge states.