Monte Carlo renormalization group Calculations for polymers

A simple method based on Wilson's renormalization group ideas is applied to calculate the dynamical critical exponentz for polymer chains in different dynamical regimes. It is shown that the Doi-Edwards reptating chain does not belong to the same dynamical universality class as the Rouse chain. The earlier results based on (4 –d, d space dimensionality) expansion for chains with excluded volume effect are recovered without any expansion. When combined with the Monte Carlo techniques, this method results in a simple scheme for calculating the static and dynamic exponents for a polymer chain with a prescribed dynamics. Numerical results suggest that the slithering snake model of Wall and Mandel for the dynamics is in a different dynamic universality class than the Rouse chain.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.Research supported in part by the National Science Foundation (Grant No. DMR-8112968) and the Petroleum Research Fund, administered by the American Chemical Society.     

Equation of Motion in Hybrid Monte Carlo

The equation of motion and molecular dynamics for simulating lattice field theory using the Hybrid Monte Carlo (HMC) algorithm are described. Some techniques for improving the HMC efficiency are discussed.     

Exact and Monte Carlo computations on a lattice model for change of conformation of a polymer

Conformational changes of linear polymers are studied by means of dynamic lattice models. The relaxation rates for the following four parameters describing the conformation of the polymer are studied for various polymer lengths: the square of the end-to-end distance, the square of the radius of gyration, thex component of the end-to-end vector, and the number of windings.In the most realistic models the relaxation rates for the first three of the above-mentioned properties decrease approximately proportional to the square of the number of monomers in agreement with the well-known Rouse model, while the relaxation of the winding number appears to be independent of the polymer length. The long-range interactions due to excluded volume restrictions are found to be of only minor importance compared to the rules presented for the local movements of the polymer segments.The results are obtained by diagonalizing the Markov matrix forn = 3, 4, 5, and 6 and by Monte Carlo simulation forn = 8, 16, 32, 64, and 128, wheren is the number of monomers.     

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100² down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e ^2βJ) and not as a power law as T↦T _c = 0. Received 10 January 2001 and Received in final form 29 May 2001     

Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard Metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model.     

Two-sided bounds on the free energy from local states in Monte Carlo simulations

We show that a precise assessment of free energy estimates in Monte Carlo simulations of lattice models is possible by using cluster variation approximations in conjunction with the local states approximations proposed by Meirovitch. The local states method (LSM) utilizes entropy expressions which recently have been shown to correspond to a converging sequence of upper bounds on the thermodynamic limit entropy density (i.e., entropy per lattice site), whereas the cluster variation method (CVM) supplies formulas that in some cases have been proven to be, and in other cases are believed to be, lower bounds. We have investigated CVM-LSM combinations numerically in Monte Carlo simulations of the two-dimensional Ising model and the two-dimensional five-states ferromagnetic Potts model. Even in the critical region the combination of upper and lower bounds enables an accurate and reliable estimation of the free energy from data of a single run. CVM entropy approximations are therefore useful in Monte Carlo simulation studies and in establishing the reliability of results from local states methods.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

一种适于光学实现的非线性神经网络模型及其蒙特卡洛学习算法

本文用计算机仿真研究了一种适于光学实现的非线性神经网络模型的存储客量α_c和寻址能力,提出了一个改进其触突互联矩阵的蒙特卡洛学习算法.数值研究表明,经过学习修正后的神经网络模型的寻址能力及存储容量都有较大的改进.     

反应堆蒙特卡罗临界模拟中均匀裂变源算法的改进

在反应堆pin-by-pin精细建模及蒙特卡罗模拟计算研究中, 由于不同栅元的功率密度差异较大, 导致蒙特卡罗方法临界计算的样本在不同栅元之间的分配不均衡, 由此引起栅元内的各种计数的统计误差差异较大. 为使大部分栅元内计数的统计误差降至一个合理的水平, 单纯增加总样本已不是一个高效的解决方法. 通过在特定临界计算迭代算法的基础上改进并实现均匀裂变源算法的思想, 对大亚湾压水堆pin-by-pin模型取得了具有较高效率的数值结果. 本工作为具有自主知识产权的蒙特卡罗粒子输运模拟软件JMCT最终达到反应堆pin-by-pin模型(包括一系列国际基准模型)的模拟性能要求提供了一个有效的工具.     

Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints

We study a new Monte Carlo algorithm for generating self-avoiding walks with variable length (controlled by a fugacity) and fixed endpoints. The algorithm is a hybrid of local (BFACF) and nonlocal (cut-and-paste) moves. We find that the critical slowing-down, measured in units of computer time, is reduced compared to the pure BFACF algorithm: _CPU N^2.3 versus N^3.0. We also prove some rigorous bounds on the autocorrelation time for these and related Monte Carlo algorithms.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk

The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates self-avoiding walks (SAWs) in a canonical (fixed-N) ensemble with free endpoints (hereN is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one effectively independent sample can be produced in a computer time of orderN. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on self-avoiding walks in two and three dimensions. Our estimates for critical exponents are=0.7496±0.0007 ind=2 and= 0.592±0.003 ind=3 (95% confidence limits), based on SAWs of lengths 200N10000 and 200N 3000, respectively.     

Spark-based improved Basin-Hopping Monte Carlo algorithm for structural optimization of alloy clusters

CoPt alloy clusters are promising candidates for catalysts in fuel-cell applications because of their enhanced catalytic performances compared with pure Pt clusters. In this article, an improved Basin-Hopping Monte Carlo (BHMC) algorithm is proposed to optimize the stable structures of CoPt clusters with different sizes and compositions, and the Spark parallel framework is employed to accelerate the structural optimizations. The results show that the improved BHMC algorithm has higher probability to find the lowest-energy structure and more rapid convergence than the traditional BHMC one. Through the comparison of different threads during Spark parallel computing, it is found that the acceleration ratio increases with the thread number while decreases for large cluster due to the limitation of the resource allocation. By investigating the optimized structures of CoPt clusters, it is revealed that for small CoPt clusters, the most stable structures exhibit a wide variety at different Co/Pt ratios; for large CoPt clusters, however, their structures are independent of the Co/Pt ratios and close to the results of their monometallic counterparts. Besides, for all the CoPt clusters, Pt atoms tend to distribute near the surface and Co atoms are generally located in the interior.     

A generalized optimization of Monte Carlo particle transport schemes

Formulations and algorithms for optimizing biased random walk problems in radiation transport are described. A matrix-integral equation is constructed by coupling the second moment and its derivative with respect to the biasing parameter. The optimization is based on estimation of the second moment around the score and the Monte Carlo perturbation algorithm to treat the variation in the biasing parameter.     

Kinematics of multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonianþ(), the absence of critical slowing down can only be expected if the expansion of þ( +) in terms of the shift contains no relevant (mass) term. We also introduce a multigrid update procedure for non-abelian lattice gauge theory and study the acceptance rates for gauge groupSU(2) in four dimensions.     

在BEPCⅡ/BESⅢ上寻找胶子球的Monte Carlo研究

在即将建造的BEPCⅡ BESⅢ上利用MonteCarlo模拟研究了J ψ→γX→γηη′(η′→γρ0 ,ρ0 →π+ π-,η→γγ)过程.研究显示BESⅢ的良好性能和大统计量的J ψ事例样本为寻找胶子球态的一些候选者并确认其存在提供了可能.基于所研究的衰变道,为BESⅢ电磁量能器晶体BGO和CsI的选择及磁场强度的选择提供了数据.     

Monte Carlo study of self-avoiding surfaces

Two models of self-avoiding surfaces on the cubic lattice are studied by Monte Carlo simulations. Both the first model with fluctuating boundary and the second one with a fixed boundary are found to belong to the universality class of branched polymers. The algorithms as well as the methods used to extract the critical exponents are described in detail. The results are compared to other recent estimates in the literature.     

A new random-number generator for multispin Monte Carlo algorithms

We develop a novel multispin coded random number generator algorithm to compute bits equal to 1 with probabilityp. Compared to previously used algorithms, this generator is at least equally fast and allows for an arbitrary accuracy of the computed probability without any significant increase in time. An explicit implementation of the algorithm is given for a Cray-1 vector computer, and the modifications for other machines are discussed. Finally, the algorithm is tested by computing the magnetization of the two-dimensional Ising model. The measured speed of the program is 57 million spin-flips per second. The agreement with theoretical values is found to remain very satisfying even when quite close (-0.5%) to the critical temperature.     

Nonergodicity of local,length-conserving Monte Carlo algorithms for the self-avoiding walk

It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local,N-conserving elementary moves is nonergodic (hereN is the number of bonds in the walk). Indeed, for largeN, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk.     

Exact Monte Carlo for few-fermion systems

We have reconsidered the fundamental difficulties of fermion Monte Carlo as applied to few-body systems. We conclude that necessary ingredients of successful algorithms include the following: There must be equal populations of random walkers that carry positive and negative weights. The positions of positive walkers should be selected from a distribution that uses Green's functions to couple all walkers. The positions of negative walkers should be generated from those of positive walkers by means of odd permutations. The correct importance functions that take into account the global interactions of the populations are different for positive and negative walkers. Use of such importance functions breaks the symmetry that otherwise would exist between configurations (of the entire population) and configurations derived by interchanging positive and negative walkers. Based upon these observations, we have constructed a stable and accurate algorithm that solves a fully-polarized, three-dimensional, three-body model problem.