Order-disorder criticality, wetting, and morphological phase transitions in the irreversible growth of far-from-equilibrium magnetic films

An exhaustive numerical investigation of the growth of magnetic films in confined (d+1)-dimensional stripped geometries (d=1,2) is carried out by means of extensive Monte Carlo simulations. Films in contact with a thermal bath at temperature T, are grown by adding spins having two possible orientations and considering ferromagnetic (nearest-neighbor) interactions. At low temperatures, thin films of thickness L are constituted by a sequence of well-ordered domains of average length l_DL. These domains have opposite magnetization. So, the films exhibit “spontaneous magnetization reversal” during the growth process. Such reversal occurs within a short characteristic length l_R, such that l_Dl_RL. Furthermore, it is found that for d=1 the system is non-critical, while a continuous order-disorder phase transition at finite temperature takes place in the d=2 case. Using standard finite-size scaling procedures, the critical temperature and some relevant critical exponents are determined. Finally, the growth of magnetic films in (2+1) dimensions with competing short-range magnetic fields acting along the confinement walls is studied. Due to the antisymmetric condition considered, an interface between domains with spins having opposite orientation develops along the growing direction. Such an interface undergoes a localization–delocalization transition that is the precursor of a wetting transition in the thermodynamic limit. Furthermore, the growing interface also undergoes morphological transitions in the growth mode. A comparison between the well-studied equilibrium Ising model and the studied irreversible magnetic growth model is performed throughout. Although valuable analogies are encountered, it is found that the non-equilibrium nature of the latter introduces new and rich physical features of interest.     

Non-equilibrium wetting transition in a magnetic Eden model

Magnetic Eden clusters (Ausloos et al., Europhys. Lett. 24, 629 (1993)) with ferromagnetic interaction between nearest-neighbor spins are grown in a confined 2d-geometry with short range magnetic fields acting on the surfaces. The change of the growing interface curvature driven by the field and the temperature is identified as a non-equilibrium wetting transition and the corresponding phase diagram is evaluated. Received 27 March 2000     

Effects of a finite number of particles on the thermodynamic properties of a harmonically trapped ideal charged Bose gas in a constant magnetic field

We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.     

Random anisotropy nematic model: Connection with experimental systems

We study theoretically the phase behavior of the continuum Random Anisotropy Nematic model. A domain-type pattern is assumed to appear in a distorted nematic liquid crystal (LC) phase. We map the model parameters to physical quantities characterizing LCs confined to Controlled-Pore Glasses and LC-aerosil dispersions. The domain size dependence on the disorder strength is obtained in accordance with the Imry-Ma prediction. The model estimates for temperature shifts of the paranematic-nematic phase transition and for the critical point, where this transition ceases to exist, are compared to the available experimental results.Received: 28 March 2004, Published online: 29 June 2004PACS: 61.30.-v Liquid crystals - 61.30.Dk Continuum models and theories of liquid crystal structure - 61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects on order - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions     

Phase transitions and interface fluctuations in double wedges and bi-pyramids with competing surface fields

The interplay between surface and interface effects on binary AB mixtures that are confined in unconventional geometries is investigated by Monte Carlo simulations and phenomenological considerations. Both double-wedge and bi-pyramid confinements are considered and competing surface fields are applied at the two opposing halves of the system. Below the bulk critical temperature, domains of opposite order parameter are stabilized at the corresponding corners and an interface runs across the middle of the bi-partite geometry. Upon decreasing the temperature further one encounters a phase transition at which the AB symmetry is broken. The interface is localized in one of the two wedges or pyramids, respectively, and the order parameter is finite. In both cases, the transition becomes discontinuous in the thermodynamic limit but it is not a first-order phase transition. In an antisymmetric double wedge geometry the transition is closely related to the wedge-filling transition. Choosing the ratio of the cross-section L × L of the wedge and its length L _y according to L _y /L ³ = const., simulations and phenomenological consideration show that the new type of phase transition is characterized by critical exponents α = 3/4, β = 0, and γ = 5/4 for the specific heat, order parameter, and susceptibility, respectively. In an antisymmetric bi-pyramid the transition occurs at the cone-filling transition of a single pyramid. The important critical fluctuations are associated with the uniform translation of the interface and they can be described by a Landau-type free energy. Monte Carlo results provide evidence that the coefficients of this Landau-type free energy exhibit a system-size dependence, which gives rise to critical amplitudes that diverge with system size and result in a transition that becomes discontinuous in the thermodynamic limit.     

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.     

Thermodynamic analysis on the stability and evolution mechanism of self-assembled quantum dots

A quantitative thermodynamic model addressing the stability and evolution mechanism during growth process of quantum dots (QDs) in Stranski-Krastanow (SK) system is established by taking into account the thickness-dependent surface energy of wetting layer (WL). It is found that the thickness-dependent surface energy of WL prevents QDs from growing up without limit. The competition between relaxation energy of QDs and thickness-dependent surface energy of WL results in a puzzling phenomenon that WL not only can hardly capture atoms to grow, but also need release atoms into QDs during deposition process and annealing. Agreement between theoretical results and experiments implies that the established thermodynamic model could be expected to be a general approach to pursue the physical mechanisms of self-assembly of quantum dots.     

Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects

We present a detailed study on the finite size scaling behaviour of thermodynamic properties for small systems of particles embedded in a reservoir. Previously, we derived that the leading finite size effects of thermodynamic properties for small systems scale with the inverse of the linear length of the small system, and we showed how this can be used to describe systems in the thermodynamic limit [Chem. Phys. Lett. 504, 199 (2011)]. This approach takes into account an effective surface energy, as a result of the non-periodic boundaries of the small embedded system. Deviations from the linear behaviour occur when the small system becomes very small, i.e. smaller than three times the particle diameter in each direction. At this scale, so-called nook- and corner effects will become important. In this work, we present a detailed analysis to explain this behaviour. In addition, we present a model for the finite size scaling when the size of the small system is of the same order of magnitude as the reservoir. The developed theory is validated using molecular simulations of systems containing Lennard-Jones and WCA particles, and leads to significant improvements over our previous approach. Our approach eventually leads to an efficient method to compute the thermodynamic factor of macroscopic systems from finite size scaling, which is for example required for converting Fick and Maxwell–Stefan transport diffusivities.     

Ising cubes with enhanced surface couplings

Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor interactions and enhanced couplings between surface spins are studied. In particular, at the surface transition, the corner magnetization shows nonuniversal, coupling-dependent critical behavior in the thermodynamic limit. Results on the critical exponent of the corner magnetization are compared to previous findings on two-dimensional Ising models with three intersecting defect lines.     

The absence of phase transition for the classical XY-model on Sierpiński pyramid with fractal dimension D=2

For the spin models with continuous symmetry on regular lattices and finite range of interactions, the lower critical dimension is d?=?2. In two dimensions the classical XY-model displays Berezinskii–Kosterlitz–Thouless (BKT) transition associated with unbinding of topological defects (vortices and antivortices). We perform a Monte Carlo study of the classical XY-model on Sierpiński pyramids (SPs) whose fractal dimension is D = log?4/log?2?=?2 and the average coordination number per site is ≈ 7. The specific heat does not depend on the system size which indicates the absence of a long-range order. From the dependence of the helicity modulus on the cluster size and on boundary conditions, we draw a conclusion that in the thermodynamic limit there is no BKT transition at any finite temperature. This conclusion is also supported by our results for linear magnetic susceptibility. The lack of finite temperature phase transition is presumably caused by the finite order of ramification of SP.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

微纳复合结构表面稳定润湿状态及转型过程的热力学分析

自然界中的微纳复合结构超疏水表面由于其独特的润湿性质引起了人们的广泛关注, 大量实验研究表明了仿生人工微纳复合结构表面润湿性能的优越性, 然而液滴在微纳复合结构表面的润湿状态和转型过程的理论研究还并不完善. 本文首先用热力学方法分析了液滴在微纳复合结构表面可能存在的所有状态(四种稳定润湿状态和五种亚稳态到稳定态转型中的过渡态), 推导出了相应的能量表达式及表观接触角方程; 基于最小能量原理, 确定液滴在微纳复合结构表面的稳定状态, 较以往模型相比, 能够更好的预测已有的实验结果; 其次研究了微纳结构尺寸对稳定润湿状态和亚稳态到稳定态转型过程的影响; 最后提出了微纳复合结构表面设计原则, 即确定“超疏水稳定区”尺寸范围, 为超疏水表面的制备提供理论依据.     

Dynamics of Condensation in the Totally Asymmetric Inclusion Process

We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric dynamics which have not been studied before, and which we also compare to exact solutions for symmetric systems. We identify all relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. The second moment of the occupation numbers is a suitable observable to characterise the transition, and exhibits a power law scaling in this regime before saturating to stationarity following an exponential decay depending on the system size. Our results are based on heuristic derivations and exact computations for symmetric systems, and are supported by detailed simulation data.     

Anchoring and structural transitions as a function of molecular length in confined liquid crystals

Using deuteron nuclear magnetic resonance to study liquid crystals confined to cylindrical pores, an anchoring transition has been found. The transition exhibits an unexpected sharp dependence of the anchoring strength on cyanobiphenyl liquid crystal molecular length. A structural transition from a parallel axial to a planar radial configuration occurs due to an anchoring transition from planar to weakly homeotropic orientation at the walls. The anchoring strength is at a minimum near the decylcyanobiphenyl (10CB) liquid crystal length. Long chain liquid crystal configurations depend on thermal cycling and on the equilibrium atmosphere leading to a bistable SmA structure. Orientational order wetting in the isotropic phase also depends on molecular length.     

Electronic structure of asymmetric vertically coupled InAs/GaAs quantum dots

In this paper, the electronic structure of an asymmetric self-assembled vertically coupled quantum dots heterostructure has been investigated. The structure consists of two ellipsoidal quantum dot (QDs) caps made with InAs embedded in a wetting layer InAs and surrounded by GaAs. Using the strain dependent k·p theory, the energy of the two lowest states of a single electron/hole which is confined within the coupled QD structure has been calculated. As a result, it can be estimated the energy gap for different geometry parameters and for tuning the external magnetic field. The numerical results show that the energy gap is very sensitive to the size asymmetry of the structure and to the small separation distance of the dots but less sensitive to the existence of an external magnetic field and large interdot distance.     

Field theory of Ising percolating clusters

The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable field theory and identify the non-perturbative mechanism which allows the percolative transition in absence of thermodynamic singularities. The analysis is extended to the Kertész line along which the Coniglio–Klein droplets percolate in a positive magnetic field.     

Magnetic susceptibility of noninteracting fermions in a confined geometry

A model system of an ideal gas of neutral fermions in a confined geometry of different symmetry and size is theoretically examined. The behavior of these systems is found to exhibit qualitatively new features such as the oscillations in magnetic susceptibility with changing geometry size and particle density, indicating that the geometric confinement substantially affects the thermodynamic properties of the system.     

Critical wetting in the square Ising model with a boundary field

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH ₁ acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.Alexander von Humboldt-Fellow     

Der Einfluß von Spinfluktuationen auf die Sprungtemperatur eines Zweibandsupraleiters

The superconducting transition temperatureT _c of a two band superconductor in the presence of magnetic and nonmagnetic impurities as well as exchange fields is calculated using a new (8 × 8)-matrix formalism for the electron Green's function. In particular we investigate the influence of spin correlations onT _c near a magnetic phase transition. It is shown that in the strong interband phonon coupling limit the system behaves essentially as a one band superconductor. In the weak coupling limit we find typical deviations from one band theories.     

Phase transitions for an ideal Bose condensate trapped in?a?quartic potential

Based on the classification scheme of phase transitions, we study the phase transitions for an ideal Bose gas with a finite number of particles confined in a three-dimensional quartic trap. We show that the phase transition of an ideal Bose gas in the three-dimensional quartic trap is of third order for finite particle numbers, quite different from the fact that the phase transition is of first order in the thermodynamic limit. We discuss the effects of finite particle numbers on the nature of the phase transitions, and determine the dependence of transition temperature on particle number.