A Monte Carlo study of the XY model

Spin systems which have a phase transition without an order parameter, like the XY model, have great importance in physics. Here we show how it is possible to study the behaviour of such a system by computer simulation without studying the spin-spin correlation functions.     

Monte Carlo Simulations of PAC-Spectra as a General Approach to Dynamic Interactions

Time Dependent Perturbed Angular Correlations of -rays (PAC) can be used to study hyperfine interactions of a dynamic nature. However, the exact effect of the dynamic interaction on the PAC-spectrum is sometimes difficult to derive analytically. A new approach based on Monte Carlo simulations is therefore suggested, here implemented as a Fortran 90 program for simulating PAC spectra of dynamic electric field gradients of any origin. The program is designed for the most common experimental condition where the intermediate level has spin 5/2, but the approach can equally well be used for other spin states. Codes for 4 different situations have been developed: (1) Rotational diffusion by jumps; used as a test case. (2) Jumps between two states with different electric field gradients, different lifetimes and different orientations of the electric field gradient principal axes. (3) Relaxation of one state to another. (4) Molecules adhering to a surface with random rotational jumps around the axis perpendicular to the surface. To illustrate how this approach can be used to improve data-interpretation, previously published data on ^111mCd-plastocyanin and ¹¹¹Ag-plastocyanin are re-considered. The strength of this novel approach is its simplicity and generality so that other dynamic processes can easily be included by only adding new program units describing the random process behind the dynamics. The program is hereby made publicly available.     

Quantum Monte Carlo Simulations in Momentum Space

Quantum Monte Carlo(QMC)methods are power-ful numerical tools that can simulate quantum many-body problems with strong interactions among par-ticles.Among them,...     

Monte Carlo renormalization group study of the XY model

The Δβ method has been used to investigate the phase structure of the XY model. A line of fixed points was found in the low-temperature phase, while a renormalization group trajectory (one relevant and no marginal coupling parameters) in the high-temperature phase. A study of higher (3rd and 4th) order derivatives of the free energy indicate that the phase transition is of infinite order and that hyperscaling is valid for the system.     

Monte Carlo Simulations of the Yukawa One-Component Plasma

The excess free energy f of the Yukawa one-component plasma is investigated by means of Monte Carlo simulations. These simulations are performed in the canonical ensemble within hyperspherical boundary conditions and f is computed for various values of the coupling parameter in the range 0.1100 and of the screening parameter * in the range 0.1*6.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

SiC电子输运特性的Monte Carlo数值模拟

利用系综MonteCarlo法研究了2H ,4H和6HSiC的电子输运特性.在模拟中考虑了对其输运过程有着重要影响的声学声子形变势散射、极化光学声子散射、谷间声子散射、电离杂质散射以及中性杂质散射.通过计算,获得了低场下这几种不同SiC多型电子迁移率同温度的关系,并以4H SiC为例,重点分析了中性杂质散射的影响.最后对高场下电子漂移速度的稳态和瞬态变化规律进行了研究.将模拟结果同已有的实验数据进行了比较,发现当阶跃电场强度为10×106V·cm-1时,4H Sic电子横向瞬态速度峰值接近33×107cm·s^-1,6H Sic接近30×107cm·s^-1.     

Monte Carlo Simulations of the Metastability in Molecular Crystals

A measure of the non-ergodicity has been introduced for plastic phases of molecular crystals. Monte Carlo simulations of the cubic, disordered phase of cyanoadamantane have been examined from the point of view of quasi-ergotic behavior. It has been shown that the conventional way of sampling based on the Metropolis algorithm is not efficient when temperature is lowered and the crystal is put into a quenched metastable situation. New methods are required to allow the system to overcome energy barriers which separate equally important volumes in the configuration space.     

From Continuous to First Order Phase Transition in a Generalized XY Model

A generalized XY model with interaction V(θ) = 2 J{1 - [cos² (θ/2)]^p2} is studied by Monte Carlo renormalization group method on two-dimensional random triangle lattice. For p = √2, a line of fixed points has been found. It characterizes that there is a Kosterlitz-Thouless phase transition. For p = 2, a first order phase transition has been found. Both of them show the relationship between the nature of phase transition and the class of interactions.     

蒙特卡洛模拟漫辐射时两种确定表面发射方向方法的比较

介绍一种有效的确定能束发射方向的方法——切球法.分析传统方法和切球法确定发射方向的原理及实施过程,说明切球法更为方便.采用2种方法对一简单的几何模型的角系数进行蒙特卡洛计算,所得结果与文献中积分结果进行比较,说明了切球法的可行性,计算精度能满足工程要求.同时对2种方法的计算耗时进行比较,切球法可以节省计算时间.将切球法应用到复杂系统中其优越性将会得到更加充分体现.     

A Review of Monte Carlo Simulations of Polymers with PERM

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting “bad” configurations by “population control”. The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the Θ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally—as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.     

Flat Histogram Monte Carlo Simulations of Triangulated Fixed-Connectivity Surface Models

Using the Wang-Landau flat histogram Monte Carlo (FHMC) simulation technique, we were able to study two types of triangulated spherical surface models in which the two-dimensional extrinsic curvature energy is assumed in the Hamiltonian. The Gaussian bond potential is also included in the Hamiltonian of the first model, but it is replaced by a hard-wall potential in the second model. The results presented in this paper are in good agreement with the results previously reported by our group. The transition of surface fluctuations and collapsing transition were studied using the canonical Metropolis Monte Carlo simulation technique and were found to be of the first-order. The results obtained in this paper also show that the FHMC technique can be successfully applied to triangulated surface models. It is non-trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces.     

均匀分布费米系统的组态路径积分蒙特卡罗模拟

改进了组态路径积分蒙卡方法,简化采样过程,开发相应程序并对无库伦相互作用谐振子以及均匀电子气进行模拟.谐振子平衡态能量与Fermi-Dirac分布符合较好,均匀电子气平衡态能量和动量基本符合Fermi-Dirac分布规律.对两种费米子系统的研究表明,组态路径积分蒙卡方法对费米子的交换效应具有较好的描述.本文探讨了费米交换符号问题的解决途径,同时对均匀电子气模型进行研究,为后续温热稠密物质的研究奠定基础.     

A Study of Nanoparticle Aerosol Charging by Monte Carlo Simulations

A Direct Simulation Monte Carlo (DSMC) technique is applied for describing the dynamics of aerosol charging. The method is based on the transformation of known combination coefficients into charging probabilities. Changes in the particle charge distribution are computed as a stochastic game, calculating the time-step after each event. The simulations are validated by comparison with analytical solutions for unipolar aerosol diffusion charging and aerosol photocharging. The advantage of the DSMC method lies in the uncomplicated simulation of multi-dimensional systems that would result in very elaborate population balances. The DSMC method is used for simulation of the photocharging of moderately concentrated bicomponent polydisperse aerosols. By means of this method, the influence of the particle parameters (size, material) on the dynamics of the charge distribution in different size and material fractions has been studied. It is shown that charge separation between size or material fractions can be achieved for aerosol components with dissimilar work functions, while the total aerosol charge is zero.     

蒙特卡罗哈密顿新方案及其检验

蒙特卡罗哈密顿方法(MCH)是研究量子理论的数值模拟新方法, 其优点是可求出超出基态的能谱和波函数. 旧MCH方案需要自由粒子的信息, 较难推广应用于格点规范理论. 本文提出克服这个困难的新方案. 首先介绍这一方案的思想, 并以1维量子力学模型V(x)=μ²x²+λx⁴(其中μ²< 0,λ>0)为例说明实现这一新方案的具体计算步骤和方法.