On the application of the critical minimum energy subspace method to disordered systems

We discuss the recent application to strongly disordered systems of the Critical Minimum Energy Subspace (CrMES) method, used to limit the energy subspace of the Wang-Landau sampling. We compare with our results on the 3D random field Ising model obtained by a multi-range Wang-Landau simulation over the whole energy range. We point out some problems that may arise when applying the CrMES scheme to models having a complex free energy landscape.     

A Theory on Flat Histogram Monte Carlo Algorithms

The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the multicanonical and Wang-Landau algorithms. PACS number: 02.70.Tt, 02.50.Ng     

Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.     

The van Hemmen spin glass revisited

We simulated the van Hemmen spin glass model by multicanonical algorithm. The exact results for this mean-field model are reproduced. Physical quantities such as energy density, specific heat, susceptibility and order parameters are evaluated at all temperatures. We also studied an alternate model with short range interactions, which displays the many-valley picture in 2D for random variables having values ±1.On leave of the absence from Department of Physics Engineering, Hacettepe University, Ankara, Turkey.     

A new comprehensive study of the 3D random-field Ising model via sampling the density of states in dominant energy subspaces

The three-dimensional bimodal random-field Ising model is studied via a new finite temperature numerical approach. The methods of Wang-Landau sampling and broad histogram are implemented in a unified algorithm by using the N-fold version of the Wang-Landau algorithm. The simulations are performed in dominant energy subspaces, determined by the recently developed critical minimum energy subspace technique. The random-fields are obtained from a bimodal distribution, that is we consider the discrete (±Δ) case and the model is studied on cubic lattices with sizes 4≤L ≤20. In order to extract information for the relevant probability distributions of the specific heat and susceptibility peaks, large samples of random-field realizations are generated. The general aspects of the model's scaling behavior are discussed and the process of averaging finite-size anomalies in random systems is re-examined under the prism of the lack of self-averaging of the specific heat and susceptibility of the model.     

Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models

We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality’s hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected d = 3 Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.     

Phase diagram of the 3D bimodal random-field Ising model

The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier WL implementations, by handling the final stage of the WL process as an entropic sampling scheme, appropriate for the recording of the required two-parametric histograms. We test the accuracy of the proposed extrapolation scheme and then apply it to study the size-shift behavior of the phase diagram of the 3D bimodal RFIM. We present a finite-size converging approach and a well-behaved sequence of estimates for the critical disorder strength. Their asymptotic shift-behavior yields the critical disorder strength and the associated correlation length's exponent, in agreement with previous estimates from ground-state studies of the model.     

Wang-Landau study of the 3D Ising model with bond disorder

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes L in the range L=8-64L=8{-}64. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.     

Can the Pruned-Enriched Method be Used for the Simulation of Fluids?

The flat histogram version of pruned and enriched Rosenbluth method (FLATPERM) is an effective Monte Carlo method for calculating densities of states of polymers on a lattice. In this paper we generalize this method to calculate the densities of states of off-lattice systems. To demonstrate the feasibility of the approach, we perform sample calculations for the Lennard-Jones fluids. The densities of states of Lennard-Jones fluids simulated by Pruned-enriched method, i.e., the generalization of FLATPERM, agree with the densities simulated by Wang-Landau method in the range of high potential energy. However the direct extension of FLATPERM fails at low energy and a useful extension still needs to be found.     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Microcanonical equilibrium properties of chiral liquid crystals—a Monte Carlo study

Chiral liquid crystals have been investigated by means of a multicanonical Monte Carlo approach in order to characterize their phase behaviour by microcanonical equilibrium properties. The liquid crystals were described by three-dimensional lattice systems with intermolecular interactions given by the chiral Lebwohl-Lasher potential. Self-determined boundary conditions have been applied in order to enable the formation of chiral phases with equilibrium pitch. Selected thermodynamic properties, e.g. microcanonical entropy, temperature, heat capacity and a set of order parameters have been determined with dependence on microcanonical total energy. A cholesteric phase with temperature-induced helix inversion could be proven where the helical superstructure of the single component system studied changed its handedness through an infinite-pitch system. The thermodynamical behaviour in the microcanonical ensemble was found to be very similar to the behaviour in the canonical ensemble. The study of microcanonical equilibrium properties by means of multicanonical Monte Carlo simulations was shown to be a powerful tool for the study of the phase behaviour of model liquid crystals.     

飞秒强激光脉冲中氩团簇库仑爆炸特性研究

利用Bathe模型，理论模拟了氩团簇在飞秒强激光中(100 fs, 1016 W/cm2)的电离和爆炸过程.研究结果显示，在团簇尺寸较小时，离子平均能量与团簇初始半径平方成正比，爆炸机制为典型的库仑爆炸.随着团簇尺寸的增加，能量增加的速度趋缓并在一定团簇尺寸后趋于饱和.模拟结果与实验数据有较好的吻合.     

熔体初始温度对液态金属Ni凝固过程中微观结构演变影响的模拟研究

采用量子 Sutton-Chen多体势, 对熔体初始温度热历史条件对液态金属Ni快速凝固过程中微观结构演变的影响进行了分子动力学模拟研究. 采用双体分布函数g(r)曲线、键型指数法、原子团类型指数法和三维可视化等分析方法对凝固过程中微观结构的演变进行了分析. 结果表明: 熔体初始温度对凝固微结构有显著影响, 但在液态和过冷态时的影响并不明显, 只有在结晶转变温度T_c附近才开始充分显现出来. 体系在1×10¹² K/s的冷速下, 最终均形成以1421和1422键型或面心立方(12 0 0 0 12 0)与六角密集(12 0 0 0 6 6) 基本原子团为主的晶态结构. 末态时, 不同初始温度体系中的主要键型和团簇的数目有很大的变化范围, 且与熔体初始温度的高低呈非线性变化关系. 然而, 体系能量随初始温度呈线性变化关系, 初始温度越高, 末态能量越低, 其晶化程度越高. 通过三维可视化分析进一步发现, 在初始温度较高的体系中, 同类团簇结构的原子出现明显的分层聚集现象, 随着初始温度的下降, 这种分层现象将被弥散开去. 可视化分析将更有助于对凝固过程中微观结构演变进行更为深入的研究. 关键词： 液态金属Ni 熔体初始温度 微观结构 分子动力学模拟     

Magnetic phase diagram for CuMn

To study the magnetic phases of CuMn, we carry out a generalized perturbation expansion of the band energy across the composition range. We obtain the pair energy using the orbital peeling technique of Burke, based on the tight-binding linear muffin-tin orbital and augmented space recursion methods. We analyze the phases of the system by studying the probability distribution of the local staggered occupation ’fields’ within a mean-field approach. We show that our predicted phase boundaries agree well with experimental results.     

Self-organized Monte Carlo localization of critical point via linear filtering

Self-organized Monte Carlo simulations are suggested. Their essence is artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by biased random walk in temperature space. The action of walker is driven by feedback utilizing the linear filtering recursion based on the instantaneous estimates of Binder cumulants. The simulation for 2d Ising model demonstrates that the mean temperature typical for the steady noncanonical equilibrium regime properly approximates the true critical temperature. The estimates of the critical Binder cumulants and critical exponents are also discussed.     

Percolation properties of the antiferromagnetic Blume-Capel model in the presence of a magnetic field

The problem of order-order and order-disorder transitions in the system described by the 2D antiferromagnetic Blume-Capel model in the presence of a magnetic field is studied by the Wang and Landau flat-histogram simulation method and by the classical Monte Carlo. Anomalous thermodynamic characteristics in low temperatures indicate different type orderings in finite temperatures. The existence of pure antiferromagnetic phases as well as mixed state is shown by detailed phenomenological analysis of the system. The border lines on the phase diagram between various orderings are determined by the complementary microscopic study of the percolation problem for c(2×2) elementary structures of antiferromagnetic ordered phases. This new approach has also shown a full agreement between the percolation threshold for the cluster of mixed phase and the critical temperature of the ordered system.     

Rotation-vibration energy cluster formation in XH2D and XHD2 molecules (X = Bi, P, and Sb)

We investigate theoretically the energy cluster formation in highly excited rotational states of several pyramidal XH₂D and XHD₂ molecules (X = Bi, P, and Sb) by calculating, in a variational approach, the rotational energy levels in the vibrational ground states of these species for J?70. We show that at high J the calculated energy levels of the di-deuterated species XHD₂ exhibit distinct fourfold cluster patterns highly similar to those observed for H₂X molecules. We conclude from eigenfunction analysis that in the energy cluster states, the XHD₂ molecule rotates about a so-called localization axis which is approximately parallel to one of the X-D bonds. For the mono-deuterated XH₂D isotopologues, the rotational spectra are found to have a simple rigid-rotor structure with twofold clusters.     

Wang-Landau study of the critical behavior of the bimodal 3D random field Ising model

We apply the Wang-Landau method to the study of the critical behavior of the three-dimensional random field Ising model with a bimodal probability distribution. For high values of the random field intensity we find that the energy probability distribution at the transition temperature is double peaked, suggesting that the phase transition is of first order. On the other hand, the transition looks continuous for low values of the field intensity. In spite of the large sample to sample fluctuations observed, the double peak in the probability distribution is always present for high fields.     

One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper

Atomic-scale computer simulation has been used to study the thermally activated atomic transport of self-interstitial atoms (SIAs) in the form of planar clusters in pure Cu and f-Fe. There is strong evidence that such clusters are commonly formed in metals during irradiation with high-energy particles and play an important role in accumulation and spatial distribution of surviving defects. An extensive study of the mobility of SIA clusters containing two to 331 interstitials has been carried out using the molecular dynamics simulation technique for the temperature range from 180 to 1200 K. The results obtained show that clusters larger than three to four SIAs are one-dimensionally mobile in both Cu and Fe. Large clusters of more than 100 SIAs in Cu and 300 SIAs in Fe have significantly reduced mobility. The problem of describing one-dimensional (1D) motion in three-dimensional space is discussed. An attempt is made to describe the mobility of SIA clusters within the approximation of 1D diffusion. For clusters in both metals the effective migration energy of 1D diffusion as estimated via the jump frequency of the cluster centre of mass is found to be independent of the number of SIAs in the clusters, although the cluster jump frequency decreases with increasing cluster size. Mechanisms of 1D mobility of interstitial clusters are discussed.     

气体团簇离子束装置的设计及其在表面平坦化、自组装纳米结构中的应用

根据超声膨胀原理,n(10-10^4)个气体原子可以绝热冷却后凝聚在一起形成团簇,经过离化后,形成带一个电荷量的团簇离子,比如Arn^+.当团簇离子与固体材料相互作用时,由于平均每个原子携带的能量(~eV)较低,仅作用于材料浅表面区域,因此,气体团簇离子束是材料表面改性的优良选择.本文介绍了一台由武汉大学加速器实验室自主研制的气体团簇离子束装置,包括整体构造、工作原理及实验应用.中性团簇束由金属锥形喷嘴(F=65-135μm,q=14°)形成,平均尺寸为3000 atoms/cluster,经离化后,其离子束流达到了50μA.Ar团簇离子因其反应活性较低,本文运用Ar团簇离子(平均尺寸为1000 atoms/cluster)进行了平坦化和自组装纳米结构的研究.单晶硅片经Ar团簇离子束处理后,均方根粗糙度由初始的1.92 nm降低到0.5 nm,同时观察到了束流的清洁效应.利用Ar团簇离子束的倾斜(30°-60°)轰击,在宽大平坦的单晶ZnO基片上形成了纳米波纹,而在ZnO纳米棒表面则形成了有序的纳米台阶,同时,利用二维功率谱密度函数分析了纳米结构在基片上的表面形貌和特征分布,并计算了纳米波纹的尺寸和数量.