共查询到20条相似文献,搜索用时 62 毫秒
1.
Weilun Jiang 《中国物理 B》2022,31(4):40504-040504
We systematically test the performance of several Monte Carlo update schemes for the (2+1)d XY phase transition of quantum rotor model. By comparing the local Metropolis (LM), LM plus over-relaxation (OR), Wolff-cluster (WC), hybrid Monte Carlo (HM), hybrid Monte Carlo with Fourier acceleration (FA) schemes, it is clear that among the five different update schemes, at the quantum critical point, the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error, and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones. These results bestow one with the necessary knowledge of extending the quantum rotor model, which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z2 topological order, to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models. 相似文献
2.
Stefan Schnabel Wolfhard Janke Michael Bachmann 《Journal of computational physics》2011,230(12):4454-4465
The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid–solid and solid–solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method. 相似文献
3.
N. Rajewsky L. Santen A. Schadschneider M. Schreckenberg 《Journal of statistical physics》1998,92(1-2):151-194
The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because of its many applications, e.g., in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel, and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest an MPA for that case and derive the corresponding matrix algebra. 相似文献
4.
We propose a method for treating in Monte Carlo simulations the problem of the induced dipoles for polarizable particle fluids confined in slab geometry and subject to an external field. In order to compute the local field in a reasonable time, a partial update of the induced dipole moments is performed by introducing a cut-off distance, as in bulk systems. This strategy is then combined with a slab adapted 3D-Ewald summation for treating the long-range interactions between the induced dipoles. The method is illustrated by simulations of confined binary mixtures in the canonical and grand canonical ensembles. 相似文献
5.
Theoretical investigation of total-asymmetric simple exclusion processes with attachment and detachment 下载免费PDF全文
In this paper, traffic systems with attachment and detachment have been studied by total-asymmetric simple exclusion processes (TASEPs). Attachment and detachment in a one-dimensional system is a type of complex geometry that is relevant to biological transport with the random update rule. The analytical results are presented and have shown good agreement with the extensive Monte Carlo computer simulations. 相似文献
6.
We apply the recently suggested linear updating algorithm of Kennedy and Kuti to four-dimensional SU(3) bosonic gauge theory with the Wilson action. The change in the action for each link update is estimated stochastically, and we find that the algorithm gives the mean plaquette correctly for reasonable parameter values. Our results indicate that this method should be efficient for Monte Carlo computations with complicated “improved” actions, and they also show the feasibility of using such “noisy” methods to include the dynamical effects of fermions. 相似文献
7.
We discuss a class of reversible, discrete approximations to Hamilton's equations for use in the hybrid Monte Carlo algorithm and derive an asymptotic formula for the step-size-dependent errors arising from this family of approximations. For lattice QCD with Wilson fermions, we construct several different updates in which the effect of fermion vacuum polarization is given a longer time step than the gauge field's self-interaction. On a 44 lattice, one of these algorithms with an optimal choice of step size is 30% to 40% faster than the standard leapfrog update with an optimal step size. 相似文献
8.
Patrick S. Brantley 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(4):599-618
We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined. 相似文献
9.
V. Ruiz Barlett J.J. Bigeón M. Hoyuelos H.O. Mártin 《Journal of computational physics》2009,228(16):5740-5748
We consider biased diffusion in a one-dimensional lattice and compare results obtained with fixed time step and kinetic Monte Carlo methods. Spurious dispersion and particle position correlation appear with the fixed time step Monte Carlo approach. The mentioned correlation increases with time. We demonstrate that the correct results, that correspond to a time step that tends to zero, are obtained using the kinetic Monte Carlo method. The conclusions also apply to biased diffusion in two or more dimensions and to random deposition. 相似文献
10.
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. 相似文献
11.
We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, p = 1-e(-J/k(B)T), in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm. 相似文献
12.
S. Kumar P. Majumdar 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(4):571-579
We suggest and implement a new Monte Carlo strategy for correlated models
involving fermions strongly coupled to classical degrees of freedom, with
accurate handling of quenched disorder as well. Current methods
iteratively diagonalise the
full Hamiltonian for a system of N sites with computation time
τN ∼N4. This limits achievable sizes to N ∼100. In
our method
the energy cost of a Monte Carlo update is computed from
the Hamiltonian of a cluster, of size Nc, constructed around the reference
site, and embedded in the larger system. As MC steps sweep over the system,
the cluster Hamiltonian also moves, being reconstructed at each site where
an update is attempted. In this method
τN,Nc
∼NNc3.
Our results are obviously exact when Nc=N,
and converge quickly to this asymptote with increasing Nc, particularly
in the presence of disorder.
We provide detailed benchmarks
on the Holstein model and the double exchange
model. The `locality' of the energy cost, as evidenced by our results,
suggests that several important but inaccessible problems can now be handled
with control. This method forms the basis of our studies in Europhys. Lett.
68, 564 (2004), Phys. Rev. Lett. 94, 136601 (2005), and
Phys. Rev. Lett. 96, 016602 (2006). 相似文献
13.
In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin- models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed. 相似文献
14.
Benchmark measurements and simulations of dose perturbations due to metallic spheres in proton beams
Monte Carlo simulations are increasingly used for dose calculations in proton therapy due to its inherent accuracy. However, dosimetric deviations have been found using Monte Carlo code when high density materials are present in the proton beamline. The purpose of this work was to quantify the magnitude of dose perturbation caused by metal objects. We did this by comparing measurements and Monte Carlo predictions of dose perturbations caused by the presence of small metal spheres in several clinical proton therapy beams as functions of proton beam range and drift space. Monte Carlo codes MCNPX, GEANT4 and Fast Dose Calculator (FDC) were used. Generally good agreement was found between measurements and Monte Carlo predictions, with the average difference within 5% and maximum difference within 17%. The modification of multiple Coulomb scattering model in MCNPX code yielded improvement in accuracy and provided the best overall agreement with measurements. Our results confirmed that Monte Carlo codes are well suited for predicting multiple Coulomb scattering in proton therapy beams when short drift spaces are involved. 相似文献
15.
We give results for the energy of the 4He and 16O nuclei using the auxiliary field diffusion Monte Carlo and a path constraint. We compare the results with previous FHNC and cluster Monte Carlo calculations.Received: 1 November 2002, Published online: 15 July 2003PACS:
21.10.Dr Binding energies and masses - 21.60.Ka Monte Carlo models 相似文献
16.
We exactly rewrite the Z(2) lattice gauge theory with standard plaquette action as a random surface model equivalent to the untruncated set of its strong coupling graphs. We simulate such surfaces including Polyakov line defects that are moved by worm-type update steps. Our Monte Carlo algorithms for the graph ensemble are reasonably efficient but not free of critical slowing down. Polyakov line correlators can be measured in this approach with small relative errors that are independent of the separation. As a first application our results are confronted with effective string theory predictions. In addition, the excess free energy due to twisted boundary conditions becomes an easily accessible observable. Our numerical experiments are in three dimensions, but the method is expected to work in any dimension. 相似文献
17.
N. V. Prokof’ev B. V. Svistunov I. S. Tupitsyn 《Journal of Experimental and Theoretical Physics》1998,87(2):310-321
We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be
formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none
of the configuration update procedures contain small parameters. We find that the most effective update strategy involves
the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green’s function. Being based
on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers,
and to calculate any dynamical correlation function as easily as expectation values of, e.g., total energy. The principles
found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions,
and in principle also make it possible to simulate continuous systems exactly.
Zh. éksp. Teor. Fiz. 114, 570–590 (August 1998)
Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor. 相似文献
18.
We calculate the ground-state energy of (4)He, (8)He, (16)O, and (40)Ca using the auxiliary field diffusion Monte Carlo method in the fixed-phase approximation and the Argonne v(6)' interaction which includes a tensor force. Comparison of our light nuclei results to those of Green's function Monte Carlo calculations shows the accuracy of our method for both open and closed-shell nuclei. We also apply it to (16)O and (40)Ca to show that quantum Monte Carlo methods are now applicable to larger nuclei. 相似文献
19.
20.
An easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced. The theoretical basis for the algorithm is developed. As an illustration we apply the method to the Lennard-Jones liquid near the triple point. We show that an acceptance ratio of 0.2 is twice as efficient for the purpose of generating a satisfactory sample as is an acceptance ratio of 0.5. There is a strong correlation between the efficiency measure and the diffusion rate of liquid particles during the simulation. We argue that the optimal value of the acceptance ratio is calculable from short Monte Carlo simulations. The method is very general and is applicable to Monte Carlo simulations involving arbitrary potentials. 相似文献