Showing papers on "Quantum Monte Carlo published in 1984"
01 Jan 1984
TL;DR: A simple introduction to Monte Carlo simulation and some specialized topics can be found in this article, where Monte Carlo studies of Critical and Multicritical Phenomena and Monte Carlo Calculations in Lattice Gauge Theories are discussed.
Abstract: 1. A Simple Introduction to Monte Carlo Simulation and Some Specialized Topics.- 2. Recent Developments in the Simulation of Classical Fluids.- 3. Monte Carlo Studies of Critical and Multicritical Phenomena.- 4. Few- and Many-Fermion Problems.- 5. Simulations of Polymer Models.- 6. Simulation of Diffusion in Lattice Cases and Related Kinetic Phenomena.- 7. Roughening and Melting in Two Dimensions.- 8. Monte Carlo Studies of "Random" Systems.- 9. Monte Carlo Calculations in Lattice Gauge Theories.- 10. Recent Developments.- Additional References with Titles.
697 citations
TL;DR: In this paper, a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets is presented, and a weak first-order isotropicnematic transition is observed.
Abstract: We present the results of a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets. A weak first order isotropicnematic transition is observed. The equation of state in the isotropic regime is compared with several current theories, none of which is found to be fully satisfactory. The density dependence of the nematic order parameter is found to be compatible with a ‘critical’ exponent β=0·25. A study of the fluctuations of the order parameter in the isotropic phase casts doubt on the applicability of the Landau-de Gennes expression for the free energy. We observe that the relation between the nematic order parameters and is compatible with the predictions of mean-field theory. Practical aspects of the computation are discussed. A novel method to compute the pressure in a constant-volume Monte Carlo run is presented.
601 citations
TL;DR: This work considers the Monte Carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region and considers the class of Markovian methods considered, which are potentially superior to conventional rejection techniques for large dimensional regions.
Abstract: We consider the Monte Carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region. The class of Markovian methods considered generate points asymptotically uniformly distributed within the region. Computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions.
524 citations
TL;DR: In this paper, the antiferromagnetic Heisenberg model on the two-dimensional triangular lattice is studied both by topological analysis of defects and by Monte Carlo simulation, and it is shown that the order parameter space of this model is isomorphic to the three-dimensional rotation group SO(3) due to the inherent frustration effect.
Abstract: Ordering process of the antiferromagnetic Heisenberg model on the two-dimensional triangular lattice is studied both by topological analysis of defects and by Monte Carlo simulation. It is shown that the order parameter space of this model is isomorphic to the three-dimensional rotation group SO(3) due to the inherent frustration effect. Homotopy analysis shows that the system bears a topologically stable point defect characterized by a two-valued topological quantum number and exhibits a phase transition driven by the dissociation of the vortices. A Monte Carlo study on the specific heat and the behavior of vortices strongly suggests the occurence of a Kosterlitz-Thouless-type phase transition. It is, however, argued that in contrast to the two-dimensional X Y model, the spin-correlation function decays exponentially even in the low-temperature phase. In order to distinguish the high- and low-temperature phases qualitatively, we introduce a “vorticity function” analogously to the Wilson loop in the quark...
266 citations
TL;DR: In this paper, a simple free energy functional, which incorporates both local thermodynamics and short ranged correlations, is formulated and applied to the calculation of the density profile of fluids near hard walls.
Abstract: A simple free energy functional, which incorporates both ‘local’ thermodynamics and short ranged correlations, is formulated and applied to the calculation of the density profile of fluids near hard walls. For hard sphere fluids the calculated profiles are in reasonable agreement with Monte Carlo results. For a Lennard-Jones liquid the profiles exhibit the phenomenon of wetting by gas; the oscillations in the density profiles become much less pronounced and a layer of gas develops near the wall as the bulk density approaches its value at coexistence. Such behaviour was found earlier in Monte Carlo simulations but is not accounted for by existing integral equation theories based on closures of the wall-particle Ornstein-Zernike equation.
240 citations
TL;DR: In this article, a random walk algorithm is presented which exactly calculates the properties of a many-electron system, and both the Green's function Monte Carlo method and nodal relaxation have been employed.
Abstract: A random walk algorithm is presented which exactly calculates the properties of a many‐electron system. For that purpose both the Green’s function Monte Carlo method and nodal relaxation have been employed and both are described in detail. The scheme is applied to several small molecules, (H3, LiH, Li2, H20) and with modest computational effort and simple importance functions, ground state energies are obtained which agree with experimental energies within statistical error bars. The small energy decrease due to nodal release is accurately evaluated by a difference method.
228 citations
222 citations
IBM1
TL;DR: In this article, a Monte Carlo calculation for light intensities scattered from a random Gaussian-correlated surface is presented for the first time, and it is shown that small randomness on a grating surface can considerably change the intensities and, in particular, the surface polariton resonances.
Abstract: A Monte Carlo calculation for light intensities scattered from a random Gaussian-correlated surface is presented for the first time. It is shown that small randomness on a grating surface can considerably change the intensities and, in particular, the surface polariton resonances. These results should be used to check perturbation-theory calculations.
191 citations
177 citations
TL;DR: In this article, Monte Carlo calculation of path integrals of non-relativistic quantum systems is applied to the N-body problem and the importance sampling of permutation and coordinates is used to avoid the negative sign problem.
Abstract: Thermodynamic properties of non-relativistic quantum systems are treated by the Monte Carlo calculation of path integrals. This method can be applied to the N-body problem. For boson systems the importance sampling of permutation and coordinates is efficient. For fermion systems direct calculation of determinant of propagators is efficient to avoid the negative sign problem.
165 citations
TL;DR: In this article, a method for estimating the importance function in forward Monte Carlo particle transport calculations is described, where the importance functions are estimated for every region of phase-space, and some deep penetration calculations are included to demonstrate applicability.
Abstract: A method for estimating the importance function in forward Monte Carlo particle transport calculations is described. The importance function is estimated for every region of phase-space. Although subject to statistical fluctuations, the estimated importance function has proven to be a very valuable tool for selecting variance reduction parameters. Some deep penetration calculations are included to demonstrate applicability.
TL;DR: In this paper, the path integral Monte Carlo (PIMC) method is used to simulate liquid neon at T = 40 K and it is shown that quantum effects are not negligible and that when the quantum effective pair potential is used in a classical molecular dynamics simulation, the results obtained for the radial distribution function agrees with that predicted by a full PIMC simulation.
Abstract: The path integral Monte Carlo (PIMC) method is used to simulate liquid neon at T=40 K It is shown that quantum effects are not negligible and that when the quantum effective pair potential is used in a classical molecular dynamics simulation the results obtained for the radial distribution function agrees with that predicted by a full path integral Monte Carlo simulation The validity of this procedure is further shown by comparing the results obtained by this method to experimental measurements of liquid neon at T=35 K
TL;DR: In this article, Monte Carlo Fourier path integral methods have been used for equilibrium statistical mechanics and their use in chemical dynamics, and it is argued that such techniques offer a practical, direct route to complex temperature density matrix elements necessary to implement recent quantum reactive flux formalisms.
Abstract: Monte Carlo Fourier path integral methods are discussed, both with respect to their use for equilibrium statistical mechanics and to their use in chemical dynamics. It is argued that such techniques offer a practical, direct route to complex temperature density matrix elements necessary to implement recent quantum reactive flux formalisms. Applications to a one‐dimensional test problem (the Eckart barrier) are discussed. A simple (classical) approximation scheme involving a temperature‐dependent effective potential is also considered.
TL;DR: By expanding Feynman path integrals in a Fourier series, a practical Monte Carlo method was developed to calculate the thermodynamic properties of interacting systems obeying quantum Boltzmann statistical mechanics as discussed by the authors.
Abstract: By expanding Feynman path integrals in a Fourier series a practical Monte Carlo method is developed to calculate the thermodynamic properties of interacting systems obeying quantum Boltzmann statistical mechanics. Working expressions are developed to calculate internal energies, heat capacities, and quantum corrections to free energies. The method is applied to the harmonic oscillator, a double‐well potential, and clusters of Lennard‐Jones atoms parametrized to mimic the behavior of argon. The expansion of the path integrals in a Fourier series is found to be rapidly convergent and the computational effort for quantum calculations is found to be within an order of magnitude of the corresponding classical calculations. Unlike other related methods no special techniques are required to handle systems with strong short‐range repulsive forces.
TL;DR: In this paper, path integral Monte Carlo methods are used to study the effect of quantization of the orientational degrees of freedom of water (H2O), using the ST2 model.
01 Jan 1984
TL;DR: A review of Quantum Monte Carlo Methods and Results for Coulombic Systems can be found in this paper, along with some applications of a new Stochastic method in Lattice Theories.
Abstract: Droplets of 4He Atoms.- Maximum Overlap Jastrow Wave Function of the Lennard Jones Bose Fluid.- Optimization and the Many-Fermion Problem.- Droplets of 3He Atoms.- Random Walk in Fock Space.- A Review of Quantum Monte Carlo Methods and Results for Coulombic Systems.- Can Monte Carlo Methods Achieve Chemical Accuracy?.- Chemical Physics of Molecular Systems in Condensed Phases.- Study of an F Center in Molten KCl.- Path Integral Monte Carlo.- A Quantum Monte Carlo Method for the Heisenberg Spin System.- Monte Carlo Simulation of One Dimensional Quantum Systems.- Monte Carlo Calculation of the Thermodynamic Properties of Quantum Lattice Models.- Numerical Simulation of Quantum Lattice Systems: Electron-Electron and Electron-Phonon Interactions in One Dimension.- The Spectrum of Pure Gauge Theories.- Evaluation of Hadron Masses in Quantum Chromodynamics.- Some Applications of a New Stochastic Method in Lattice Theories.
TL;DR: In this article, the effect of electron-electron correlations on the solitons in electron-phonon models of quasi-one-dimensional materials was studied, and it was shown that the ground state of an odd chain, singly charged or neutral, is a soliton.
Abstract: We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that ''soliton doping'' persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.
CERN1
TL;DR: In this article, the quantitative behavior of the β -function of the SU(3) Wilson action is studied with the help of a systematically optimized Monte Carlo Renormalization Group method.
TL;DR: In this article, the dynamic Monte Carlo renormalization group was applied to the Glauber kinetic Ising model and the dynamical critical exponent z was found by simulation of up to 81922 and 5123 spins on the vector computer CDC Cyber 205, using the new 'Method of 2D colours' for the Monte Carlo part.
Abstract: Applying the dynamic Monte Carlo renormalisation group to the Glauber kinetic Ising model, the dynamical critical exponent z is found by simulation of up to 81922 and 5123 spins on the vector computer CDC Cyber 205, using the new 'Method of 2d colours' for the Monte Carlo part (update speed 22 megaspins/s). The two-dimensional result z=2.14-or+0.02 disagrees with Domany's hypothesis (1984). For three dimensions, a systematic trend in z with increasing blocksize leads to an extrapolated value z=1.965-or+0.010, which is consistent with a theoretically expected value 2.02.
TL;DR: In this article, a harmonic reference system for Monte Carlo evaluation of discretized path integrals is developed and various equilibrium averages are calculated for a one-dimensional quartic oscillator, and compared to converged basis set results.
Abstract: A harmonic reference system for Monte Carlo evaluation of discretized path integrals is developed. Various equilibrium averages are calculated for a one‐dimensional quartic oscillator, and compared to converged basis set results; it is shown that use of the reference system substantially decreases the number of discretized points (relative to the free particle reference system) necessary to compute accurate quantum mechanical expectation values.
TL;DR: In this paper, Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature.
Abstract: Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature. The internal energy of both the ordered and disordered phases is fitted by appropriate series expansions, and the free energy is obtained analytically from the series. The ordering transition is seen to be of first order with a transition temperature of 1.736\ifmmode\pm\else\textpm\fi{}0.001 in units of the nearest-neighbor coupling $J$. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be $\ensuremath{\sim}2.5a$. The behavior of the correlation length is approximately mean-field-like.
TL;DR: In this paper, a simple detailed Monte Carlo procedure, based on the continuous slowing down approximation together with the Wentzel model of the atom, is shown to give results in good agreement with experiment and with more involved Monte Carlo calculations.
Abstract: A simple detailed Monte Carlo procedure, based on the continuous slowing down approximation together with the Wentzel model of the atom, is shown to give results in good agreement with experiment and with more involved Monte Carlo calculations. Energy straggling is reproduced by means of the Lenz inelastic cross-section and the distribution of energy losses found in the classical theory of binary collisions.
TL;DR: In this paper, a new Monte Carlo technique for the calculation of the function y = g exp (βu) is proposed for hard body systems, especially suitable at low and moderate densities and separations below the contact.
Abstract: A new Monte Carlo technique for the calculation of the function y = g exp (βu) is proposed for hard body systems. The method is especially suitable at low and moderate densities and separations below the contact. The y-function was calculated for hard spheres and hard diatomics. For hard spheres surprisingly small deviations from Grundke-Henderson formula were found. For the diatomics at Ls = 0·6 radial slices at four special orientations were determined. The applicability of the proposed method and of the umbrella sampling technique due to Patey and Torrie are compared.
TL;DR: In this paper, the metropolis algorithm for numerical simulation of configurations, widely used nowadays for lattice gauge theories, is applied to the evaluation of path integrals of quantum mechanics.
TL;DR: In this article, Monte Carlo simulations of very large systems (up to 17*109 lattice sites) and series analysis are studied by showing that the value of the correction-to-scaling exponent is slightly lower at the percolation threshold than away from it.
Abstract: Corrections to scaling for percolation cluster numbers in two dimensions are studied by Monte Carlo simulations of very large systems (up to 17*109 lattice sites) and by series analysis. Both series and Monte Carlo work suggests that the value of the correction-to-scaling exponent is slightly lower at the percolation threshold than away from it. Moreover, the corrections to scaling observed at pc ( Omega equivalent to 0.64) might be due to the mixing of scaling fields rather than to the irrelevant scaling fields. The Monte Carlo results are compatible with finite-size scaling, and finite-size scaling corrections are estimated. Technical problems associated with Monte Carlo simulation of very large systems are discussed in an appendix.
TL;DR: In this paper, a Monte Carlo sampling technique was used for direct evaluation of interfacial tension over a wide range of system sizes and temperatures, and an accurate estimate for the surface tension amplitude in excellent agreement with Onsager's exact result was obtained.
Abstract: We present a novel application of Monte Carlo sampling techniques for the direct evaluation of the interfacial tension that is applicable over a wide range of system sizes and temperatures. The results for the two-dimensional Ising model with system size up to 32 \ifmmode\times\else\texttimes\fi{} 32 for temperature at and below ${T}_{c}$ have been analyzed within scaling theory. An accurate estimate for the surface-tension amplitude in excellent agreement with Onsager's exact result is obtained.
TL;DR: The possibility of representing the orientational correlations in a dipolar fluid by an effective pair potential, U eff(r), depending only on the separation r, is considered in this article.
Abstract: The possibility of representing the orientational correlations in a dipolar fluid by an effective pair potential, U eff(r), depending only on the separation r, is considered U eff(r) is obtained from the two-particle orientational partition function by series expansion and direct numerical integration methods for a wide range of interaction strengths Free energies are obtained for the dipolar hard sphere fluid by use of the GvdW theory of simple fluids and compared with Monte Carlo simulation results The coexistence curve is also obtained and compared with Monte Carlo, Pade and MSA results The critical temperature is overestimated by about 30 per cent but the critical volume agrees well with the simulation estimate