Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed. Received 22 April 1999     

Magnetic properties and critical behavior of quasi-2D layered Cr4Te5 thin film

Quasi-2D layered Cr₄Te₅ thin film has attracted great attention because it possesses the high Curie temperature close to room temperature and relatively large saturation magnetization. However, the magnetic interactions and the nature of magnetic phase transition in the Cr₄Te₅ film have not been explored thoroughly. In this paper, we focused on the critical behavior of its magnetic phase transition through the epitaxial Cr₄Te₅ film fabricated by pulsed laser deposition (PLD). The final critical exponents β = 0.359(2) and γ = 1.54(2) were obtained by linear extrapolation together with Arrott-Noakes equation of state, and their accuracy was confirmed by using the Widom scaling relation and scaling hypothesis. We find that some magnetic disorders exist in the Cr₄Te₅ film system, which is related to Cr₄Te₅ critical behavior why its critical behavior is quite far from any conventional universality class. Furthermore, we also determined that the Cr₄Te₅ film exhibits a quasi-2D long-range magnetic interaction. Finally, the itinerant ferromagnets of Cr₄Te₅ films were confirmed by the Takahashi’s self-consistent renormalization theory of spin fluctuations. Our work provides a new idea for understanding the mechanism of magnetic interactions in similar 2D layered films.     

Scaling of waves in the bak-tang-wiesenfeld sandpile model

We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>/=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk and boundary waves by means of their correspondence to spanning trees, and by extensive numerical simulations. While the scaling behavior of avalanches is complex and usually not governed by simple scaling laws, we show that the probability distributions for waves display clear power-law asymptotic behavior in perfect agreement with the analytical predictions. Critical exponents are obtained for the distributions of radius, area, and duration of bulk and boundary waves. Relations between them and fractal dimensions of waves are derived. We confirm that the upper critical dimension D(u) of the model is 4, and calculate logarithmic corrections to the scaling behavior of waves in D=4. In addition, we present analytical estimates for bulk avalanches in dimensions D>/=4 and simulation data for avalanches in D相似文献   

Phase transitions of bilayer spin-1/2 Baxter-Wu model with repulsive interlayer interactions

Using a Monte Carlo simulation and the single histogram reweighting technique, we study the critical behaviors and phase transitions of the Baxter-Wu model on a two-layer triangular lattice with repulsive interlayer interactions. Via the finite-size analysis, we obtain the transition temperatures and critical exponents at different interlayer coupling strengths. The reduced energy cumulants and the histograms reveal pseudo-first-order phase transitions, and the critical exponents derivate from the standard Baxter-Wu model if the coupling is weak. As the increase of the coupling, the behavior of the pseudo-first order transition disappears and the critical exponents are in accordance with the ones known for the 2D 4-state Potts model.     

Kinetic growth mechanisms of sputter-deposited Au films on mica: from nanoclusters to nanostructured microclusters

Au nanostructured film was deposited on mica by room temperature RF sputtering. The growth mechanism of the film was studied analyzing the evolution of the film morphology as a function of its thickness by the atomic force microscopy. In the early stages of a growth the film evolution proceeds by the nucleation and growth of nanoclusters. After a critical thickness the growth of microclusters formed by the joining of nanoclusters in preferential nucleation sites, onto a quasicontinuous film, is observed. We quantified the evolution of the mean nanoclusters height and surface density and of the film roughness. This data were analyzed by the dynamic scaling theory of growing interfaces obtaining the scaling and roughness exponents z and β whose values suggest a conservative growth process. We also quantified the growth of the microclusters showing that it is consistent with a coalescence/impingement dynamic. About the formation of the microclusters, furthermore, we speculate that their origin is strongly correlated to the features of the sputtering technique in connection with the deposition on a high-diffusivity substrate.     

Monte Carlo simulation code for confocal 3D micro‐beam X‐ray fluorescence analysis of stratified materials

Stratified materials are of great importance for many branches of modern industry, e.g. electronics or optics and for biomedical applications. Examination of chemical composition of individual layers and determination of their thickness helps to get information on their properties and function. A confocal 3D micro X‐ray fluorescence (3D µXRF) spectroscopy is an analytical method giving the possibility to investigate 3D distribution of chemical elements in a sample with spatial resolution in the micrometer regime in a non‐destructive way. Thin foils of Ti, Cu and Au, a bulk sample of Cu and a three‐layered sandwich sample, made of two thin Fe/Ni alloy foils, separated by polypropylene, were used as test samples. A Monte Carlo (MC) simulation code for the determination of elemental concentrations and thickness of individual layers in stratified materials with the use of confocal 3D µXRF spectroscopy was developed. The X‐ray intensity profiles versus the depth below surface, obtained from 3D µXRF experiments, MC simulation and an analytical approach were compared. Correlation coefficients between experimental versus simulated, and experimental versus analytical model X‐ray profiles were calculated. The correlation coefficients were comparable for both methods and exceeded 99%. The experimental X‐ray intensity profiles were deconvoluted with iterative MC simulation and by using analytical expression. The MC method produced slightly more accurate elemental concentrations and thickness of successive layers as compared to the results of the analytical approach. This MC code is a robust tool for simulation of scanning confocal 3D µXRF experiments on stratified materials and for quantitative interpretation of experimental results. Copyright © 2011 John Wiley & Sons, Ltd.     

Hydrophobic switching nature of methylcellulose ultra-thin films: thickness and annealing effects

We have studied the thermosensitive property of methylcellulose (MC) thin films supported on Si substrate by static sessile drop contact angle measurements, and their surface properties and thin film structure by x-ray reflectivity (XRR) and atomic force microscopy (AFM) techniques. From the static sessile drop contact angle measurements, the MC thin films showed the characteristic hydrophilic-to-hydrophobic transition at ～70?°C, which is the lower critical solution temperature of the bulk solution volume phase separation transition. For films with thickness d ≤ R(g), the onset of such a transition is affected by the film thickness while very thick films, d ? R(g), yielded higher contact angles. Annealing the MC thin films with thicknesses ～200 ? (near the radius of gyration, R(g), of the polymer) below the bulk glass transition temperature (T(g) ～ 195?° C) would not change the hydrophobic switch nature of the film but annealing 'at' and above the bulk T(g) would change its surface property. From surface topography images by AFM, there were no significant changes in either the roughness or the film texture before and after annealing. With XRR data, we were able to determine that such changes in the surface properties are highly correlated to the film thickness changes after the annealing process. This study, we believe, is the first to examine the thermal annealing affects on the thermal response function of a thermoresponsive polymer and is important for researching how to tailor the hydrophobic switching property of MC thin films for future sensing applications.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.     

Exploring magnetic properties of ultrathin epitaxial magnetic structures using magneto-optical techniques

We describe magneto-optic Kerr effect studies of ultrathin Fe and Ni films on single crystal surfaces of Ag and Cu. Monolayer Fe films on Ag(100) exhibit the theoretically predicted spin-orbit anisotropy, but also yield some interesting discrepancies between behavior predicted by Kerr effect and by spin-polarized photoemission experiments. Layer-dependent studies of the magnetic moment of Ni on Ag(111) and Ag(100) suggest sp-d hybridization effects quench the first layer magnetic moment on Ag(111) but not on Ag(100). Temperature dependent studies of thin film magnetization obtained from Kerr effect measurements yield thickness dependent Curie temperatures, and critical exponents for several thin film systems.     

Critical exponents of the random-field O(N) model

The critical behavior of the random-field Ising model has long been a puzzle. Different methods predict that its critical exponents in D dimensions are the same as in the pure (D-2)-dimensional ferromagnet with the same number of the magnetization components contrary to the experiments and simulations. We calculate the exponents of the random-field O(N) model with the (4+epsilon)-expansion and obtain values different from the exponents of the pure ferromagnet in 2+epsilon dimensions. An infinite set of relevant operators missed in previous studies leads to a breakdown of the (6-epsilon)-expansion.     

弥散边缘型分形金簿膜的临界特性

研究了沉积在分形基底上的弥散边缘型分形金薄膜的边缘对三次谐波系数以及临界电流的影响．结果表明，该薄膜系统的三次谐波系数、电阻率以及临界电流之间仍存在指数式临界关系．但由于边缘的影响，其临界指数与其它薄膜系统的相应值之间存在着较大差别．还对这些临界规律的普适性问题进行了讨论     

A new analytical model of high voltage silicon on insulator （SOI） thin film devices

A new analytical model of high voltage silicon on insulator (SOI) thin film devices is proposed, and a formula of silicon critical electric field is derived as a function of silicon film thickness by solving a 2D Poisson equation from an effective ionization rate, with a threshold energy taken into account for electron multiplying. Unlike a conventional silicon critical electric field that is constant and independent of silicon film thickness, the proposed silicon critical electric field increases sharply with silicon film thickness decreasing especially in the case of thin films, and can come to 141V/μm at a film thickness of 0.1μm which is much larger than the normal value of about 30V/μm. From the proposed formula of silicon critical electric field, the expressions of dielectric layer electric field and vertical breakdown voltage (V_B,V) are obtained. Based on the model, an ultra thin film can be used to enhance dielectric layer electric field and so increase vertical breakdown voltage for SOI devices because of its high silicon critical electric field, and with a dielectric layer thickness of 2μm the vertical breakdown voltages reach 852 and 300V for the silicon film thicknesses of 0.1 and 5μm, respectively. In addition, a relation between dielectric layer thickness and silicon film thickness is obtained, indicating a minimum vertical breakdown voltage that should be avoided when an SOI device is designed. 2D simulated results and some experimental results are in good agreement with analytical results.     

Critical adsorption and dimensional crossover in epitaxial FeCo films

The critical behavior of thin FeCo films grown on MgO has been studied using phase-sensitive synchrotron x-ray diffraction. These studies unravel several novel features of criticality in thin films, as the simultaneous appearance of the 3D-2D crossover and the truncation of the correlation length normal to the film at approximately 1/3 of the film thickness. Above the critical temperature of the film we observe a pronounced pinning of the order parameter at the MgO-FeCo interface, which indicates a novel critical adsorption behavior.     

Critical behavior of three-state Potts model on decagonal covering quasilattice

The three-state Potts model on a 2D decagonal covering quasilattice is investigated by means of the Monte Carlo simulation. The periodic boundary conditions are realized on a rhombus-like covering pattern. By use of the finite-size scaling analysis, we obtain the critical temperature and the critical exponents. The critical temperature is higher than that of the square lattice mainly due to the larger mean coordination number of the covering model. The critical exponents are close to the corresponding values of the 2D periodic lattices, which means that the Potts model on the covering structure may belong to the same universal class as that of the periodic lattices.     

Crystalline order in superfluid (3)He films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).     

The wrong kind of gravity

The KPZ formula [V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819] shows that coupling central charge c≤1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of Φ³ planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins.Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the “wrong” c value. We might then expect to see the critical exponents appropriate to the c value used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the Ising, tricritical Ising and 3-state Potts models.     

Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions

Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model.     

N-cluster correlations in four- and five-dimensional percolation

We study N-cluster correlation functions in four- and five-dimensional (4D and 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E72, 016126 (2005)] using the disjoint-set data structure, and simulate a cylindrical geometry L^d−1 × ∞, with the linear size up to L = 512 for 4D and 128 for 5D. We determine with a high precision all possible N-cluster exponents, for N =2 and 3, and the universal amplitude for a logarithmic correlation function. From the symmetric correlator with N=2, we obtain the correlationlength critical exponent as 1/ν=1.4610(12) for 4D and 1/ν=1.737(2) for 5D, significantly improving over the existing results. Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge. Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.     

Quantum critical dynamics simulation of dirty boson systems

Recently, the scaling result z=d for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in order to determine the actual value of z. We study a model of quantum bosons at T=0 with disorder in 2D using highly effective worm Monte?Carlo simulations. Our data analysis is based on a finite-size scaling approach to determine the scaling of the quantum correlation time from simulation data for boson world lines. The resulting critical exponents are z=1.8±0.05, ν=1.15±0.03, and η=-0.3±0.1, hence suggesting that z=2 is not satisfied.