A stochastic model of three-dimensional crystal growth

This paper describes a stochastic model of crystallization from a gas or dilute solution. The model is limited to a crystal of rectangular symmetry whose surface has nonzero Miller indices. By a mapping into the modified KDP model, the kinetic growth coefficient can be given approximately as an analytic function of the Miller indices of the surface. Numerical simulations indicate that the aproximation is accurate within a few percent at all surface orientations.     

开边界六顶角模型的边界关联函数

讨论了具有开边界六顶角模型的关联函数，计算了涉及边界自发极化的边界关联函数，得到了它们的行列式表示. 关键词： 六顶角模型 关联函数 开边界     

Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representation of the partition function of the six-vertex model with a non-diagonal reflecting end under domain wall boundary condition.     

The Bethe ansatz for the six-vertex model with rotated boundary conditions

A method is suggested for derivation of the Bethe ansatz equations for the six-vertex model on a square lattice rotated at an arbitrary angle with respect to the coordinate axes. The method is based on the random walk representation for configurations of the model. The equations for the ice model on the rotated lattice are derived and some numerical results are obtained.     

The asymmetric six-vertex model

The exact solution of the asymmetric six-vertex model, published nearly without derivation by Sutherlandet al. in 1967, is rederived in detail. The transfer matrix method and the Bethe Ansatz solution for the free energy (which can be calculated from an integral equation) are discussed. For some special cases (zero or maximal polarization) the integral equation can be solved exactly. In addition, an asymptotic analysis, valid for small but nonzero polarization, is carried out. The analytical properties of the results and their relevance for the BCSOS model are discussed.     

Chiral Potts model as a descendant of the six-vertex model

We observe that theN-state integrable chiral Potts model can be considered as a part of some new algebraic structure related to the six-vertex model. As a result, we obtain a functional equation which is supposed to determine all the eigenvalues of the chiral Potts model transfer matrix.     

Rigorous derivation of domain growth kinetics without conservation laws

The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we show that the average lifetime of such a domain is proportional to its area. We also consider theT=0 dynamics of a single infinite quadrant. The area of the quadrant decreases during the time evolution, and we show that the area lost grows linearly with time. We solve a first passage time problem as well. That is, we calculate the average time it takes for the area lost to reach a given value for the first time. Lastly, we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical six-vertex model.     

Growth in a restricted solid on solid model with correlated noise

We introduce correlated growth into a restricted solid on solid model (RSOS), a stochastic deposition model with a constraint on neighboring height differences. A two-dimensional lattice model is used in which particles are deposited via horizontal Levy flight steps with a step length distribution exponentf. Though RSOS is in the same universality class as ballistic deposition for uncorrelated deposition, it appears to depart from it for strong correlations. Forf=1, the short-range limit is reached and both exponents and, which describe the dependence of surface width on time and strip length, tend to 1. Forf>1 we retreat to an enhanced algorithm, searching for growth sites which become excessively rare. We find an unusual short-time dependence, but still tends to 1. The number of growth sitesG shows saturation forf<1, while forf1 we observeG/L0 as the strip lengthL increases. Finally, we test directly the relationship of noise-noise correlation strength tof, and find that a direct comparison between correlated growth models and theoretical predictions for growth with correlated noise is so far unjustified.     

Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {–1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential in the limit of zero temperature; we analyze the first excursion from the metastable –1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2 is crossed.     

The conical point in the ferroelectric six-vertex model

We examine the last unexplored regime of the asymmetric six-vertex model: the low-temperature phase of the so-called ferroelectric model. The original publication of the exact solution by Sutherland, Yang, and Yang and various derivations and reviews published afterward do not contain many details about this regime. We study the exact solution for this model by numerical and analytical methods. In particular, we examine the behavior of the model in the vicinity of an unusual coexistence point that we call the conical point. This point corresponds to additional singularities in the free energy that were not discussed in the original solution. We show analytically that at this point many polarizations coexist, and that unusual scaling properties hold in its vicinity.     

噪声对均质形核过程影响的晶体相场法研究

采用晶体相场模型,模拟了有色噪声诱发的均质形核过程. 结果表明,噪声强度在一定范围内对系统平衡热力学参量、形核势垒、临界晶核尺寸影响甚微; 而对形核孕育时间影响较大,形核孕育时间随噪声强度的增大呈指数减小趋势. 进一步分析表明,噪声对形核孕育时间的影响主要是由于噪声的引入改变了原子动力学系数.     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.     

体心立方固溶体合金中的"团簇+连接原子"结构模型

为体现固溶体合金中的溶质原子产生的化学短程序,文章提出了配位数为14的团簇在体心立方(bcc)点阵中的堆垛模式,并建立了基于bcc结构的"团簇+连接原子"结构模型,用团簇成分式[团簇](连接原子)_x表述. 此模型中,与基体组元具有相对大的负混合焓的溶质原子占据团簇心部,其他原子作为连接或者替代团簇壳层基体原子. 1 ∶1结构模型[团簇](连接原子)₁由于最大程度地保证了团簇与连接原子的近邻,构成了连接原子最有效的合金化方式. 在两个实用bcc固溶体合金体系中, 1 ∶1模型指导设计了低V含量的储氢合金 V₁和低弹性模量高强度的 Nb₁合金. 关键词： 体心立方固溶体成分设计 "团簇+连接原子"结构模型 Ti-Cr-V合金 Ti-Zr-Mo-Nb合金     

Kinetic Monte Carlo simulation of thin film growth

A three-dimensional kinetic Monte Carlo technique has been developed for simulating growth of thin Cu films. The model involves incident atom attachment, diffusion of the atoms on the growing surface, and detachment of the atoms from the growing surface. The related effect by surface atom diffusion was taken into account. A great improvement was made on calculation of the activation energy for atom diffusion based on a reasonable assumtion of interaction potential between atoms. The surface roughness and the relative density of the films were simulated as the functions of growth substrate temperature and film thickness. The results showed that there exists an optimum growth temperatureT _opt at a given deposition rate. When the substrate temperature approaches toT _opt, the growing surface becomes smoothing and the relative density of the films increases. The surface roughness minimizes and the relative density saturates atT _opt. The surface roughness increases with an increment of substrate, temperature when the temperature is higher thanT _opt.T _opt is a function of the deposition rate and the influence of the deposition rate on the surface roughness depends on the substrate temperatures. The simulation results also showed that the relative density decreases with the increasing of the deposition rate and the average thickness of the film.     

Subdominant critical singularities in the bcc Ising model

In order to analyze coalescing singularities using series expansion, a modification of the method introduced by Baker and Hunter is proposed. The Padé approximants on the Mellin transform are computed simultaneously for the initial series and its derivatives, allowing unbiased estimates for the critical parameters. The method is applied to the series generated by Nickel for various values of the spin in the bcc Ising model. We show that even with these longer series, the subdominant indices display large variation with the spin, and remain too small compared to the universal renormalization group prediction. However, the method does not detect other singularities in the temperature plane which are responsible for the observed discrepancy. Therefore the discrepancy is not significant.     

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

On the stability of crystal growth

We investigate properties of solid-on-solid models for crystal growth, involving general microscopic rates of capture of atoms by the crystal surface and of escape of atoms. The rates in this Markov process influence the stability of the growing surface. We prove, for various different ranges of the rate parameters, stability (i.e., ergodicity) and instability (i.e., nullity) of the growth process. Symmetry properties of the process, such as reversibility, dynamic reversibility, and reflection invariance, are proved or disproved under various conditions. We give a measure of surface smoothness that distinguishes between stable and unstable growth.