Surface structures of equilibrium restricted curvature model on two fractal substrates

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature(ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension df, but possess different dynamic exponents of random walk zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk zrw. The ERC model growing on the two substrates follows the well-known Family–Vicsek scaling law and satisfies the scaling relations 2α + df≈ z ≈ 2zrw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.     

Anisotropic percolation and the d-dimensional surface roughening problem

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and δ=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. The values of δ in higher dimensions (δ=0.38±0.03 in d=4 and δ=0.27±0.05 in d=5) do not support a recent theoretical conjecture.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

Magnetic behaviour of some Mn.III2.VI4 compounds and their alloys

Measurement of the magnetic susceptibility χ as a function of temperature were made on polycrystalline samples from the alloy systems Cd_1−zMn_zGa₂Se₄, Zn_1−zMn_zGa₂Se₄ and Cd_1−zMn_zIn₂Te₄ which had been subjected to various heat treatments. The 1/χ versus T curves indicated that for the Zn---Se alloys, for all values of z, samples slowly cooled to room temperature were antiferromagnetic showing ideal Curie-Weiss behaviour, but for samples quenched from 700°C the behaviour was a mixture of antiferromagnetic and spin-glass. For the Cd---Se alloys, samples from the range (0.6 < z < 1.0) showed very similar behaviour, but in the range (0 < z < 0.6) even the very slowly cooled samples showed a mixture of antiferromagnetic and spin-glass behaviour. For the Cd---Te alloys, all samples, however heat-treated, showed spin-glass form. Values of the Curie-Weiss constant Ф were determined from all of the 1/χ versus T curves, and by comparison with the T(z) phase diagrams for the different alloy systems, the values of Ф were correlated with the ordering of the Mn atoms on the cation lattice. It is shown that the experimental values of Ф can give a very convenient way of determining the type of ordering and the degree of order in such alloys.     

The crumpling transition of crystalline random surfaces

We investigate the crumpling transition in two different models of crystalline random surfaces with extrinsic curvature which have recently caused some confusion and find that many of the results previously obtained are erroneous. Using the Fourier acceleration technique to ameliorate critical slowing down problems we have made numerical simulations of surfaces of up to 128² points embedded in three dimensions. The first model, which has a non-compact lattice version of the extrinsic curvature, suffers from a sickness in the non-crumpled phase which is a lattice artefact; it is smooth in one intrinsic direction and folded up on the scale of the lattice spacing in the other, so we call this phase corrugated. The crumpling transition is continuous, having a diverging persistence length with critical exponent v = 1.15 ± 0.15 and a cusp in the specific heat indicating that 0. The second model, in which the extrinsic curvature depends upon the cosine of the angle between normals of adjacent triangles, also has a continuous transition with v = 0.94 ± 0.20 and = 0.53 ± 0.15. Just beyond the crumpling transition, the smooth phase is found to have Hausdorff dimension d_H < 2.14 at two standard deviations and so we conclude that d_H = 2 throughout this phase. A study of the correlation functions shows that, in the crumpled phase, the system is apparently described by a very simple gaussian action. If true, this result could have important implications which we discuss briefly.     

Multilayer relaxation of Rh(311)

The multilayer relaxation of the Rh(311) surface was investigated by means of LEED structure determination both for vertical and surface parallel (registry) relaxations. Excellent agreement between experimental and calculated spectra could be achieved mirrored by a minimum Pendry R-factor R = 0.174. The first three layer spacings are oscillatorily relaxed by Δd₁₂/d₀ = −14.5 ± 1.8%, Δd₂₃/d₀ = +4.9 ±2.0% and Δd₃₄/d₀ = −1.0 ±2.0%. There seems to be a coherent registry shift of the fir Δs = 0.03 ± 0.07 Å which, however, is within the error limits of the structure determination. Moreover, an energy dependent inner potential is detected. The results are discussed in comparison to equivalent surfaces of other materials as well as for the less open surfaces of rhodium.     

Oxygen nonstoichiometry and phase transitions of the neodymium-rich Nd1+xBa2−xCu3Oz solid solution

On the basis of chemical, thermal analysis and Cu K-edge X-ray absorption measurements, oxygen content in the Nd_1+xBa_2−xCu₃O_z solid solution was determined between 1000°C in air and 400°C in oxygen for x=0.05–0.9 compositions. It has been observed that the oxygen nonstoichiometry Δz of the Nd_1+xBa_2−xCu₃O_7+x/2−Δz solid solution decreases 2–2.5 times for a large substitution (Δz≈0.3–0.33 for x=0.9), despite of the acclaimed higher total oxygen content. The difference in nonstoichiometry is explained by a higher average value of the copper oxidation state (ACV), which is vital for the solid solution with large x even at elevated temperatures (ACV≈2–2.05 for x>0.3 at 1000°C, PO₂=0.21 atm). On the contrary, the ACV after complete oxygenation is almost constant (about 2.25–2.3) for the whole series. The x-dependence of the oxygen content is not monotonous and structural phase transitions can be observed at x=0.3 and x=0.6, as confirmed by the X-ray diffraction and the Raman scattering spectroscopy. The first well-known transition is connected with the oxygen disorder due to the Nd substitution for Ba at random Ba-sites. In the present work, it is proved by the apical oxygen mode broadening in Raman spectra. Ordering of the Nd and Ba atoms with a subsequent orthorhombic distortion of the lattice may occur even at 1000°C in air due to the second transformation at x≈0.6. The invariable orthorhombicity of the Nd-rich solid solution with x>0.6 is not caused by the oxygen absorption as in the x=0.05 case. Existence of high- and low-temperature orthorhombic modifications of this solid solution has been observed for the first time. Finally, a tentative 3D (z–x–T) diagram is suggested for the Nd_1+xBa_2−xCu₃O_z solid solution up to 1000°C in air, including the new x=0.6–0.9 region.     

Spin flipping and percolation for the ±J Spin Glass at zero temperature

Examinations of the percolation properties of the domains of flipping and never flipping spins for the zero temperature dynamics of the ±J Ising Spin Glass show different results for different dimensionalities of the simulation lattice. Especially the properties or the square and the simple cubic lattice differ as far as the domains of the ‘non-equilibrium never flipping spins’ are concerned. These never flipping spins percolate in four, five and six dimensions but do not build spanning clusters in two dimensions with three dimensions being close to the border case. Therefore this quantity may be related to the Spin Glass ordering process.     

Scaling properties of eden clusters in three and four dimensions

We study the scaling properties of noise reduced Eden clusters in three and four dimensions for variant B in the strip geometry. We find that the width W for large times behaves as a(s)g(L/s^d−1), where L is the width of the strip, s the noise reduction parameter, d the dimension of space, and a(s) a decreasing function of s, g is a scaling function with the property g(u)→1/2 as u→0 and g(u)u^x as u→∞, where χ is the roughness exponent. This scaling result leads to a new way of determining χ. In 3 dimensions, our numerical values for χ support a recent conjecture by Kim and Kosterlitz: χ = 2/(d + 2), and contradict all the former analytical conjectures. In 4 dimensions, we cannot distinguish between the conjectures of Kim and Kosterlitz and the conjecture of Wolf and Kertész, because large crossovers and finite size effects make the measurement of the exponents difficult.     

Short-time dynamic behaviour of critical XY systems

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent z differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media

A model based on invasion percolation was used to simulate the migration on a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form N_s(g)s^-2ƒ(s|g|^-z where z=1+(D−1)ν(ν+1). Here D is the fractal dimensionality of invasion percolation, with trapping, and ν is the ordinary percolation correlation length exponent.     

Development of particle multiplicity distributions using a general form of the grand canonical partition function

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba–Nielson–Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.     

Dynamical scaling of the quantum Hall plateau transition

Using different experimental techniques, we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f=0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa=0.5+/-0.1, yielding a dynamical exponent z=0.9+/-0.2.     

Some properties of the spectral flow in semiriemannian geometry

Let be the action integral on a semiriemannian manifold ( , g) defined on the space of the curves z : [0, 1] → joining two given points z₀ and z₁. The critical points of ƒ are the geodesics joining z₀ and z₁. Let s ε [0, 1]. We study the behavior, in dependence of s, of the eigenvalues of the Hessian form of ƒ evaluated at z, restricted to the interval [0, s]. A formula for the derivative of the eigenvalues is given and some applications are shown.     

Critical behavior of diluted Heisenberg ferromagnets with competing interactions

The pure and the site-diluted classical Heisenberg model on the face centered cubic (fcc) lattice with ferromagnetic exchange J_nn between nearest neighbors and antiferromagnetic exchange J_nn = −J_nn/2 between next nearest neighbors is studied by Monte Carlo simulation. Data are generated by the heat bath algorithm for lattice sizes L = 4, 8, 12, 16, 20 and 24, using histogram reweighting techniques and sampling up to several hundred configurations of the random site disorder. From a finite size scaling analysis both the critical temperature and the critical exponents are estimated. For the pure system, the data are in very good agreement with the critical exponent estimates 1/v ≈ 1.42, β/v ≈ 0.51 obtained from other methods (as a check of the accuracy of our approach, we also study the nearest neighbor model — where J_nn ≡ 0− and again obtain very good agreement with the known behavior). However, for the diluted systems evidence for a new universality class is found. While for concentration c = 0.875 of occupied sites strong crossover phenomena preclude us from giving exponent estimates, for c = 0.75 we find 1/v ≈ 1.2 and β/v ≈ 0.45. Possible reasons why the Harris criterion may not apply for this system are discussed. The application of this study to experiments on Eu_xSr_1−xS is briefly mentioned.     

Scaling properties for ordered/disordered 2-D dry froths

We investigate the evolutionary behaviour of a 2-D dry froth with initial ordered/disordered conditions corresponding, respectively, to monodisperse/polydisperse topological networks. Using the direct simulation approach, we discuss the scaling properties of the cell side distribution, f(n), and its second moment, μ₂, for various system sizes and initial structures. For the case of a highly ordered network, the introduction of disorder may be viewed in terms of “seeding” the froth system with a number of defects, d, where for d = 1 previous work has shown that stable conditions are not achieved. We find that the limiting behaviour here depends on the amount of disorder, where this is quantified by the proportion of non-uniform initial cells and the pattern of seeding. Our findings support the view that a quasi-scaling state exists for the highly ordered froth, in contrast to the universal scaling state of the disordered and low-ordered froth. In the light of these results, we briefly reconsider the question of transience for the early results of Aboav (1980).     

Spectral density analysis of the chiral transition in nf=4 finite temperature QCD

We apply the spectral density reweighting technique to the analysis of the chiral phase transition in finite-temperature lattice quantum chromodynamics (QCD) with four flavors of dynamical staggered fermions and m_qa=0.025. Our simulations were performed using the hybrid Monte Carlo method for L_tL³ lattices with L_t=4 and L=6, 8 and 10. We calculate partition function zeros, as well as the maxima of the specific heat and of the susceptibilities for the Polyakov loop and for the chiral condensate. A finite size scaling analysis of these data leads to preliminary results for the critical coupling β_c, for the critical exponent ν, for the latent heat, and for the jumps in the Polyakov loop and in the chiral condensate.     

The stochastic stabilized Kuramoto-Sivashinsky equation: a model for compact electrodeposition growth

We report on numerical studies of the dynamical behavior of a stochastic version of the stabilized Kuramoto-Shivashinsky equation, in 1 + 1 dimensions, at short times and small length scales. The solution evolves as a rough growing interface, showing a well defined growth exponent β = 0.37±0.04 and a roughness exponent that saturates at a value α = 0.80±0.04. A morphological instability may also develop for certain values of the control parameter and with a well-defined characteristic length. The resulting dynamical scenario and scaling properties compare fairly well with experimental results on slow compact electrodeposition growth.