Showing papers on "Quantum Monte Carlo published in 1979"
TL;DR: The mathematical equivalence of Reggeon Field Theory with a Markov process (sometimes called Schlogl's first model) is used for Monte Carlo simulations of its critical behaviour in 1 + 1 dimensions as mentioned in this paper.
395 citations
TL;DR: In this article, a new Monte Carlo method for problems in quantum statistical mechanics is described, based on the use of iterated short-time Green's functions, for which "image" approximations are used.
Abstract: A new Monte Carlo method for problems in quantum‐statistical mechanics is described. The method is based on the use of iterated short‐time Green’s functions, for which ’’image’’ approximations are used. It is similar to the use of Feynman or Wiener path integrals but with a modification to take account of hard‐core boundary conditions. It is applied to two one‐dimensional test problems: that of a single particle in a hard‐walled box and that of two hard particles in a hard‐walled box. For these test problems, the results are in excellent agreement with exact quantum‐mechanical results both at high temperatures (near the classical limit) and at very low temperatures such that essentially only the ground state is occupied. Generalizations to three‐dimensional systems, to many‐body systems, and to more realistic potentials are discussed briefly.
321 citations
IBM1
TL;DR: In this paper, a particular Monte Carlo renormalization-group (MCRG) method is discussed, which is still in the early stages of development, but has a number of advantages over older methods, and has already produced excellent results for some systems of interest.
Abstract: In 1976, Ma1 made the suggestion of combining Monte Carlo (MC) computer simulations with a real-space renormalization-group (RG) analysis to calculate critical exponents at second-order phase transitions. Since then, numerous authors2–14 have presented various ways of implementing Ma's idea to produce a useful theoretical tool. In these lectures, I will discuss a particular Monte Carlo renormalization-group (MCRG) method that I and several coworkers have been using.7–14 The method is still in the early stages of development, but it has a number of advantages over older methods, and has already produced excellent results for some systems of interest.
213 citations
TL;DR: In this article, a Monte Carlo method is used to compute the properties of the fluid and crystal phases of the Lennard-Jones model at absolute zero, subject only to statistical sampling errors.
Abstract: A Monte Carlo method is used to compute the properties of the fluid and crystal phases of the Lennard-Jones model of $^{4}\mathrm{He}$ at absolute zero. The method yields exact results subject only to statistical sampling errors. The energy, structure factor, and momentum distribution are calculated at several densitites in both phases. In addition, in the crystal phase we have carried out a detailed study of the single-particle distribution function. The densities at which melting and freezing occurs are determined. In both phases perturbative estimates of the three-body Axilrod-Teller potential are computed. Overall the agreement with experiment is good to excellent. However there are significant discrepancies between the computed and experimental equations of state. We believe this is due to the inadequacy of the Lennard-Jones potential.
147 citations
TL;DR: The use of an approximate or idealized value for one of the factors in a transition rate must degrade the accuracy of the complete calculation, compared to the potential accuracy of a pure Monte Carlo calculation where all quantities representing the system can be exact as mentioned in this paper.
Abstract: Publisher Summary This chapter reflects the growing emphasis on the use of numerical solution by computer, in the theory of electron transport phenomena in solids. In most cases of interest, the electron system may be given a quasi-classical description. This chapter also attempts to provide a “state of the art” presentation of methods, and at the same time survey the accomplished—and some potential—applications of Monte Carlo to topics in the physics of electron transport in solids. The use of an approximate or idealized value for one of the factors in a transition rate must, to some extent, degrade the accuracy of the complete calculation, compared to the potential accuracy of a pure Monte Carlo calculation where all quantities representing the system can be exact. A measure of the error might be computed, from the auxiliary function and the Monte Carlo ensemble, at the same time as the calculation itself.
82 citations
01 Jan 1979
TL;DR: Three computational methods, the charge-simulation method, the finite-element method and the Monte Carlo method, have been programmed for practical use for calculation of electrostatic potentials and fields for realistic engineering problems.
Abstract: The paper is concerned with the calculation of electrostatic potentials and fields for realistic engineering problems Three computational methods, the charge-simulation method, the finite-element method and the Monte Carlo method, have been programmed for practical use To test their accuracy, the results obtained for a set of trial problems are compared Examples are also given that illustrate the particular capabilities of each method, and their different advantages and disadvantages are discussed
60 citations
Abstract: The problem of constructing quantum–mechanical corrections to classical equilibrium statistical–mechanical results is considered. These corrections (excluding interchange symmetry effects) can be computed within a classical framework if a temperature‐dependent effective potential is utilized. Two approaches to the construction of this potential are investigated. The first of these is a modification of an earlier procedure by Feynman. This method is similar in spirit to the empirical Pitzer–Gwinn approximation, and in fact is utilized to derive this earlier result. The second approach involves a general Monte Carlo prescription both for the construction of the effective potential and for obtaining the ratio of the quantum and classical–mechanical partition functions.
58 citations
TL;DR: In this paper, a Monte Carlo renormalization-group method is described and illustrated by application to the two-dimensional Ising model using several different renormalisation-group transformations.
Abstract: A Monte Carlo renormalization-group method is described and illustrated by application to the two-dimensional Ising model using several different renormalization-group transformations.
50 citations
TL;DR: The phase transition of the 3-dimensional 3-state Potts model at zero field was investigated by a careful Monte Carlo analysis as discussed by the authors, and the transition was found to be of first order.
Abstract: The phase transition of the three-dimensional 3-state Potts model at zero field is investigated by a careful Monte Carlo analysis. The transition is found to be of first order. Fluctuations appear to be very strong and critical exponents can be defined with reasonable accuracy. The results are compared with those of the 4-state Potts model.
47 citations
TL;DR: In this article, Monte Carlo results for a fluid of polarizable dipolar hard spheres are reported for both isotropic and anisotropic particles, and it is shown that induced forces make a large contribution to the thermodynamic properties and significantly influence the fluid structure.
Abstract: In this paper we report Monte Carlo results for a fluid of polarizable dipolar hard spheres. Both isotropic and anisotropic particles are considered. It is shown that the induced forces make a large contribution to the thermodynamic properties and significantly influence the fluid structure. The various approximate treatments of polarizable systems are evaluated and a recent theory proposed by Wertheim is found to be very successful.
44 citations
TL;DR: In this paper, the Born-Green-Yvon 2 (BGY2) theory was used to compute the hard disk and hard sphere correlation functions for triplet geometries in which two particles are held fixed at contact.
Abstract: The hard‐sphere and hard‐disk triplet correlation functions are computed from the Born–Green–Yvon 2 (BGY2) theory at several different densities for triplet geometries in which two particles are held fixed at contact. The same quantities are generated for hard spheres by means of a Monte Carlo method. Both the BGY2 and the Monte Carlo data agree satisfactorily. Next, the Kirkwood superposition approximation and the ’’one‐dimensional’’ approximation introduced earlier are examined to determine the regions of their applicability.
TL;DR: In this paper, the Green's function Monte Carlo method is generalized to treat quantum systems at non-zero temperature and a method is described, and successfully applied, whereby an importance function may be determined in large part during the Monte Carlo, rather than a priori.
TL;DR: In this paper, a universal functional form for the direct correlation function of the one-component plasma is proposed, which depends on only one scaling parameter which is determined from a novel hypernetted-chain compressibility equation through a single numerical integration.
Abstract: A universal functional form is proposed for the direct correlation function of the one-component plasma This form depends on only one scaling parameter which is determined from a novel hypernetted-chain compressibility equation through a single numerical integration The results compare well with the numerical solutions of the hypernetted-chain integral equation as well as with recent Monte Carlo computations
TL;DR: In this paper, the results of a numerical resolution of the equation for the fourth field moments by Monte Carlo methods in a turbulent medium are given, compared with experiment and asymptotic theory.
Abstract: The results of a numerical resolution of the equation for the fourth field moments by Monte Carlo methods in a turbulent medium are given. The numerical computations are compared with experiment and asymptotic theory.
TL;DR: In this article, Pandharipande et al. described the ground state of a quantum fluid in terms of the pair correlation function and pair-pair correlation function, which are the response functions to first and second order scattering respectively.
TL;DR: In this paper, an alternative Monte Carlo method, which relies on Fick's First Law is described in detail, and the results of the vacancy mechanism tracer correlation factor in the square planar, S.C., f.c., and b.c lattices were found to be at least as accurate as those obtained by the former simulation method under the same conditions of lattice dimension and total number of vacancy umps.
Abstract: The usual Monte Carlo method, which is based on the Einstein equation and employed for calculating tracer correlation factors, is discussed. An alternative Monte Carlo method, which relies on Fick's First Law is described in detail. The method is based on the calculation of the tracer flux under steady-state conditions. Upon application of the new method the results of the vacancy mechanism tracer correlation factor in the square planar, S.C., f.c.c., and b.c.c. lattices were found to be at least as accurate as those obtained by the former simulation method under the same conditions of lattice dimension and total number of vacancy umps.
TL;DR: In this paper, error prediction in non-analog Monte Carlo calculations of multiplying systems, even when supercritical, is discussed. But the present work is limited to the case of non-multiplying media.
Abstract: The Monte Carlo method for neutron transport calculations suffers, in part, because of the inherent statistical errors associated with the method. Without an estimate of these errors in advance of the calculation, it is difficult to decide what estimator and biasing scheme to use. Recently, integral equations have been derived that, when solved, predicted errors in Monte Carlo calculations in nonmultiplying media. The present work allows error prediction in nonanalog Monte Carlo calculations of multiplying systems, even when supercritical. Nonanalog techniques such as biased kernels, particle splitting, and Russian Roulette are incorporated. Equations derived here allow prediction of how much a specific variance reduction technique reduces the number of histories required, to be weighed against the change in time required for calculation of each history. 1 figure, 1 table. (RWR)
TL;DR: In this article, Monte Carlo simulations of the Edwards-Anderson-Ising spin glass with Gaussian distribution of nearest-neighbor exchange forces in four and five dimensions are performed to check the speculation thatd=4 is the lower critical dimensionality.
Abstract: Monte Carlo simulations of the Edwards-Anderson-Ising spin glass with Gaussian distribution of nearest-neighbor exchange forces in four and five dimensions are performed to check the speculation thatd=4 is the lower critical dimensionality. In contrast to this expectation we find no qualitative difference at all to the results in two and three dimensions. We still find that on not too long time-scales there is an apparently rather well defined freezing temperatureT f , where the susceptibility has a cusp, and belowT f nonzero order parametersq, ψ can be found as ford=2, 3. But even ford=5 the decay of the Edwards-Anderson order parameter belowT f is found to be consistent with a logarithmic variation over several decades of observation time. The possible interpretations of this result are discussed. Our data thus suggest that either there is no equilibrium phase transition in all these dimensions, or more likely that a phase transition exists for 2≦d≦5 but the properties of the ‘ordered phase’ may be rather peculiar.
TL;DR: In this paper, the exponential biasing method for Monte Carlo is discussed, and methods leading to the optimal choice of the various parameters involved are considered, and an approximation procedure for ascertaining optimal parameters is derived and tested.
Abstract: The exponential biasing method for Monte Carlo is discussed, and methods leading to the optimal choice of the various parameters involved are considered. Specifically, an approximation procedure for ascertaining optimal parameters is derived and tested. An examination of the physical processes underlying the method illuminates the theoretical derivation.
Journal Article•
TL;DR: In this article, the problem of analyzing the variance in a Monte Carlo calculation is addressed, and the batch analysis method is considered, where one uses the average of contributions of k particles as an independent random variable, versus the one-particle analysis method, where k = 1.
Abstract: The problem of analyzing the variance in a Monte Carlo calculation is addressed. The batch analysis method is considered, where one uses the average of contributions of k particles as an independent random variable, versus the one-particle analysis method, where k = 1. It is shown through general statistical considerations that the one-particle method yields more reliable estimates of the variance.
TL;DR: In this article, a method was developed to predict the asymptotic behavior of totally self-avoiding walks by utilizing data for random walks of limited orders of nonself intersection.
Abstract: A method is developed to predict the asymptotic behavior of totally self‐avoiding walks by utilizing data for random walks of limited orders of nonself intersection. The results shed further light on the exponent, γ, in the equation for the mean square end‐to‐end separation :
TL;DR: A review of recent progress in the numerical simulation of quantum many-body systems by Monte Carlo methods is given in this article, where the basic idea of Monte Carlo quadrature and its use in variational estimates of the energy of extensive quantum systems is recapitulated.
TL;DR: In this article, the authors derived the event value Wg ([rbar], Ω) in a form which can be obtained directly from existing adjoint Monte Carlo computer codes and used it as the path-length biasing and angular biasing in the forward Monte Carlo calculation, respectively.
Abstract: The event value Wg ([rbar], Ω) has been derived in a form which can be obtained directly from existing adjoint Monte Carlo computer codes. It is demonstrated that the event value and the point value functions obtained from the adjoint Monte Carlo calculation can be used as the path-length biasing and the angular biasing in the forward Monte Carlo calculation, respectively. The iterative forward-adjoint Monte Carlo method using the source biasings is employed to reduce the standard deviation in the shielding problem. In addition, the effectiveness of the source biasing schemes is investigated in the same problem. The results indicate a significant reduction in the standard deviation and a substantial improvement in the efficiency of the Monte Carlo shielding calculations.
TL;DR: In this paper, a method of optimizing the selection of source particle parameters in Monte Carlo calculations is developed based on using information learned from previous histories to influence the source particle parameter selection for subsequent histories and the results of a problem in which this source biasing optimization technique is applied to source energy biasing are presented.
Abstract: A method of optimizing the selection of source particle parameters in Monte Carlo calculations is developed. This method is based on using information learned from previous histories to influence the selection of source particle parameters for subsequent histories. The results of a problem in which this source biasing optimization technique is applied to source energy biasing are presented.
TL;DR: In this paper, the structure and thermodynamic properties of the quantum liquids 4He and H2 near the liquid-gas critical point are calculated with the effective potential approximation, in which the two-body Slater sum replaces the Boltzmann factor; the statistical mechanics problem is formally equivalent to that of a fictitious classical fluid.
Abstract: The structure and thermodynamic properties of the quantum liquids 4He and H2 near the liquid-gas critical point are calculated with the effective potential approximation, in which the two-body Slater sum replaces the Boltzmann factor; the statistical mechanics problem is formally equivalent to that of a fictitious classical fluid. Approximate integral equation methods from the theory of classical fluids are then used to calculate the critical point parameters and the radial distribution function g(r). The results from the approximate integral equations are compared both with experimental data and with the results of an exact Monte Carlo calculation for the fictitious fluid for a range of densities at the temperatures 7 and 8 K in 4He and 36 and 40 K in H2.
TL;DR: In this paper, the analytical expressions suitable for the Monte Carlo calculation to obtain the solution of Schrodinger's equation of the hydrogen atom in a magnetic field are developed and the energy values and the wavefunctions for the even states of m = 0 and 1 are obtained numerically and compared with other results based on the variational method.
TL;DR: In this article, the cubic model described by the Hamiltonian ⋅=−JΣ
Abstract: The cubic model, described by the Hamiltonian ⋅=−JΣ
TL;DR: In this article, the singularities of the kernels are included in the transition density of the simulated Markov chain, which enables the Neumann series for this system converges, enabling the Monte Carlo method to be used.
Abstract: AN ALGORITHM of the Monte Carlo method is constructed for solving the metaharmonic equation (1). A system of integral equations of the second kind is derived for the functions δku(x), k = 0, 1,…, n−1. It is shown that if the singularities of the kernels are included in the transition density of the simulated Markov chain, the Neumann series for this system converges, which enables the Monte Carlo method to be used. The case n = 2, x ϵ Rm, important in the theory of plasticity is discussed in detail.
20 Jul 1979
TL;DR: In this article, a class of spin systems in two dimensions with symmetry of a cyclic group is studied in three ways: by the real space renormalization group technique, by the duality transformation and by a numerical experiment.
Abstract: A class of classical spin systems in two dimensions with symmetry of a cyclic group is studied in three ways: by the real space renormalization group technique, by the duality transformation and by a numerical experiment. The former two methods are shown to be in a close relation to each other. Useful information is obtained on the shape of the critical surface, on the behavior near the criticality and on thermodynamic quantities such as the internal energy and the magnetic susceptibility. Some of these results are compared with expected properties of the planar model, to which the present model reduces if an appropriate limit is taken.