Analysis of diffuse scattering of single crystals using monte carlo methods

While conventional crystal structure analysis using Bragg intensities reveals only information about the average structure of the crystal, diffuse scattering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approaches to the analysis of diffuse scattering based on Monte Carlo methods are described in this paper: the direct Monte Carlo (MC) simulation technique and the Reverse Monte Carlo (RMC) method. The MC method requires the construction of a model for the disorder based on physical and chemical considerations and the selection of a set of near-neighbour interactions. The given model is realized by minimizing the total energy of the crystal via MC simulations. Next, the corresponding diffraction pattern is calculated and compared with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative “match” between observed and calculated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensities directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a chemically sensible structure or further insight into the particular disorder problem.

The first example given in this paper demonstrates the viability of the RMC method by refining diffuse scattering data calculated from simulated structures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffuse scattering of stabilized zirconias (CSZ) are shown, modelling occupational disorder as well as displacements.     

Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.     

MORSE程序中的MonteCarlo技巧扩充

扩充了MORSE程序的MonteCarlo技巧,针对球几何穿透概率计算,引入了三种MonteCarlo技巧,增强了MORSE程序处理屏蔽问题的能力和计算可靠性。     

Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.      

Quantum statistical monte carlo methods and applications to spin systems

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem⁽¹⁾ thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures. Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985.     

Quantum monte carlo studies of electron-electron interaction effects in conducting polymers

We discuss recent studies, using the quantum ensemble projector Monte Carlo (EPMC) method, of theoretical models of conducting polymers. Our focus is on the consequences of incorporating direct electron-electron interactions into the “standard” electron-phonon interaction models. Among the observables we examine one energetics of purely dimerized ground states, single solitons, soliton pairs, averaged spin and charge distributions, and local correlation functions.     

Monte carlo study of the interacting self-avoiding walk model in three dimensions

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.     

A monte carlo method for approximating critical cluster size in the nucleation of model systems

A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n ^2/3] is used to predict critical cluster size and critical supersaturation ratio, S^*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS ^*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.This material is based upon work supported by the National Science Foundation under Grant No. ATM80 15790 and the National Aeronautics and Space Administration under Grant No. NAS8-31150.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

A dynamical monte carlo algorithm for master equations with time-dependent transition rates

A Monte Carlo algorithm for simulating master equations with time-dependent transition rates is described. It is based on a waiting time image, and takes into account that the system can become frozen when the transition rates tend to zero fast enough in time. An analytical justification is provided. The algorithm reduces to the Bortz-Kalos-Lebowitz one when the transition rates are constant. Since the exact evaluation of waiting times is rather involved in general, a simple and efficient iterative method for accurately calculating them is introduced. As an example, the algorithm is applied to a one-dimensional Ising system with Glauber dynamics. It is shown that it reproduces the exact analytical results, being more efficient than the direct implementation of the Metropolis algorithm     

蒙特卡罗法用于机械制冷机污染传输特性的仿真计算

为了优化结构设计和建立标准的污染控制体系来提高机械制冷机的运行寿命,需要深入研究污染气体在制冷机管道内的传输机理。采用直接模拟蒙特卡罗(DSMC)方法对污染气体的传质过程进行理论仿真,设计编写软件程序,计算了分子流状态下制冷机内污染气体分子通过圆管和环形管路等微通道的传输几率。得到关键管道的传输几率小于3%,并比较了不同结构尺寸管路的传输几率。     

Do the simple and 2/3 majority models belong to the same universality class?: A monte carlo approach

We extend the majority model (introduced by Tsallis in 1982) in the sense that the required majority might be different from the simple majority. We simulate these models for typical cases which include simple and 2/3 majorities. We exhibit the average cluster size as well as the order parameter as functions ofp, the concentration of one of the two possible constituents. No crossover exists between the simple- and non-simple-majority models.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

A theoretical study of magnetic phase transitions in ultra-thin films: Application to NiO

Phase diagrams and critical temperatures of projected onto fcc (1 0 0) layers, which is believed to be applicable to first-row transition metal oxides such as VO, MnO and NiO, are obtained from mean field theory and Monte Carlo simulations. Within the regime, J_se > 0, which includes MnO and NiO, both approaches predict bicritical behaviour of the AF₂ and AF₃ antiferromagnetic spin alignments for odd numbers of layers greater than one and monocritical behaviour for even numbers of layers, even when films are described by single values of J_d and J_se. The ferromagnetic alignment, on the other hand, exhibits monocritical behaviour for all thicknesses from the monolayer through to the bulk. For values of (x = J_d/J_se) which are close to those obtained from first principles calculations for NiO and also those derived from measured magnon spectra, estimates of the thickness dependence of the critical temperature from Monte Carlo simulations are similar to that derived from linear polarised X-ray absorption spectra of NiO(1 0 0) ultra-thin films grown epitaxially on MgO(1 0 0) [D. Alders, L.H. Tjeng, F.C. Voogt, T. Hibma, G.A. Sawatzky, J. Vogel, M. Sacchi, S. Iacobucci, Phys. Rev. B 57 (1998) 11623].     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Dynamical Behavior of the Multibondic and Multicanonic Algorithm In The 3D q-State Potts Model

We investigate the dynamical behavior of the recently proposed multibondic cluster Monte Carlo algorithm in applications to the three-dimensional q-state Potts models with q= 3, 4, and 5 in the vicinity of their first-order phase transition points. For comparison we also report simulations with the standard multicanonical algorithm. Similar to the findings in two dimensions, we show that for the multibondic cluster algorithm the dependence of the autocorrelation time on the system size Vis well described by the power law V , and that the dynamical exponent is consistent with the optimal random walk estimate = 1. For the multicanonical simulations we obtain, as expected, a larger value of 1.2.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Dynamical Critical Exponent for the Majority-Vote Model

We investigate the dynamical behavior of the isotropic majority-vote model on a square lattice using a combination of damage spreading and finite-size scaling methods. For initial damage D(0)1/2, the dynamical phase diagram exhibits a chaotic-frozen phase transition at a critical noise parameter q _c =0.0818±0.0002, while for D(0)1/2 the damage does not propagate for any value of the model's parameter 0q<1/2. From simulations at q _c , we find that the dynamical critical exponent is z=0.65±0.05.     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.