Showing papers on "Dynamic Monte Carlo method published in 1982"
1,196 citations
TL;DR: In this paper, a Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored, and it is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems.
Abstract: A Monte Carlo procedure based on a discrete point representation of the path integral for the density matrix is explored. It is found that the variance of the estimator used to evaluate the energy grows as the square root of the number of discrete points used, and is therefore to be avoided in highly quantum mechanical systems, where the number of discrete points must be large. A new energy estimator based on the virial theorem is proposed and shown to be well behaved. The main points of the paper are illustrated, using the harmonic oscillator as an example.
422 citations
TL;DR: In this article, the authors derived exact statistical mechanical relations for polyelectrolyte systems within the primitive model using the cell model and determined the osmotic pressure through an explicit evaluation of the derivative of the partition function.
Abstract: Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the pressure is overestimated by 10%–50% in the cases studied, while with divalent counterions the error is substantially larger and a discrepancy of one order of magnitude is found.
282 citations
TL;DR: In this paper, the dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature of the interface is studied and the dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law.
Abstract: The dynamics of interfaces where the normal component of an interface velocity is proportional to the curvature is studied. The dynamic structure function due to the motion of random interfaces is shown to satisfy a scaling law. The results are compared with Monte Carlo simulations of the kinetics of the order-disorder transition in a quenched system.
258 citations
TL;DR: The internal energy of the classical one-component plasma is calculated using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for 1.
Abstract: We calculate the internal energy of the classical one-component plasma using a Monte Carlo technique for 128, 250, 432, 686, and 1024 particles for $1l\ensuremath{\Gamma}l300$ in order to determine the effect of a differing number of particles on the thermodynamics. By fitting the internal energy to a function of $\ensuremath{\Gamma}$ and $N$ (the particle number), we find the free energy for both the liquid and solid for an infinite number of particles.
207 citations
TL;DR: In this article, the potential energy surface of the LiH molecule was calculated using the Green's function Monte Carlo method and the calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV.
Abstract: The potential energy surface of the LiH molecule is calculated using the Green’s function Monte Carlo method. The calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV. These results are within 6% and 2% of the experimental values, respectively. The Green’s function Monte Carlo method is discussed in some detail with particular emphasis on problems of chemical interest.
165 citations
TL;DR: In this article, an improved Monte Carlo method is presented for lattice gauge theories with fermions, taking the pion mass and meson Regge trajectory slope as input, this procedure is used to calculate the rho mass on lattices up to 12 4 for gauge group¯I, the best discrete approximation to SU(2).
150 citations
TL;DR: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported in this article.
Abstract: The first numerical determination of the thermodynamic isotropic-nematic transition in a simple three-dimensional model fluid, viz., a system of infinitely thin hard platelets, is reported. Thermodynamic properties were studied with use of the constant-pressure Monte Carlo method; Widom's particle-insertion method was used to measure the chemical potential. The phase diagram is found to differ considerably from predictions of a second-virial ("Onsager") theory. Virial coefficients up to the fifth were computed; b5 is found to be negative.
133 citations
TL;DR: In this article, a Monte Carlo method for simulation of the stepwise polyreaction generating treelike polymer structures and admitting intramolecular reactions inside the largest particle (identified with the gel) has been developed.
Abstract: A Monte Carlo method for simulation of the stepwise polyreaction generating treelike polymer structures and admitting intramolecular reactions inside the largest particle (identified with the gel) has been developed. The method is equivalent to the kinetic theory of network formation applied to finite systems. The limiting properties of an infinite system are obtained by extrapolation; among those best accessible are the critical conversion of gelation and weight fractions of sol and gel. Polymerization of a trifunctional monomer with a first-shell substitution effect was used as an example to demonstrate that, with the exception of some special cases, the results obtained by the kinetic method are virtually identical with those provided by the statistical method based on the treelike model and cascade substitution.
99 citations
TL;DR: By the use of umbrella sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard-Jones liquid mixtures.
Abstract: By the use of umbrella‐sampling technique in the Monte Carlo method proposed by Torrie and Valleau, reliable data have been established for the Helmoholtz free energy of mixing in some selected models of Lennard‐Jones liquid mixtures. The variational method in perturbation theory is found to account for these Monte Carlo data. Validity of some representative semiempirical theories is discussed and it is found that none of them can reproduce the present Monte Carlo results reasonably well. Finally the phase stability of the present models is discussed in terms of both the free energy of mixing and local composition values recently obtained from our molecular dynamics calculations.
85 citations
TL;DR: In this article, a Monte Carlo procedure for studying polymer chains in concentrated solution or in the melt is described and the dependence of the rms end-to-end distance on chain length for chains on a simple cubic three-dimensional lattice with every lattice site filled.
Abstract: A Monte Carlo procedure for studying polymer chains in concentrated solution or in the melt is described. The procedure generates new configurations by breaking and reforming chains. The procedure is used to examine the dependence of the rms end‐to‐end distance on chain length for chains on a simple cubic three‐dimensional lattice with every lattice site filled. Chains with as many as 512 segments were examined. The rms end‐to‐end distance is proportional to (N−1)ν for N the number of polymer segments and for ν in the range 0.51–0.52, rather than the expected value of 1/2. However, the data seem to indicate a continuing decrease of ν with increasing N so the value 1/2 cannot yet be ruled out.
TL;DR: In this paper, the mean field estimates of the transition temperature and discontinuity of the order parameter are in good agreement with computer simulations for N = 3 and 4, and the N → ∞ limit of mean field theory has a first-order phase transition.
TL;DR: In this article, the phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. And the phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation.
Abstract: The phase diagram of the two-dimensional, three-state chiral Potts or asymmetric clock model is studied using Monte Carlo techniques. The phase boundaries are compared to those obtained using the finite-size renormalization group and the free fermion approximation. The incommensurate phase is described in detail and crossover effects near the Lifshitz point are discussed.
TL;DR: A Monte Carlo method of simulation of the grand canonical ensemble based on the concept of maximum number of molecules is applied to the 6 : 12 Lennard-Jones fluid and the results compared with Adams' [1] at T*=1·15 and 1·25 as discussed by the authors.
Abstract: A Monte Carlo method of simulation of the grand canonical ensemble based on the concept of maximum number of molecules is applied to the 6 : 12 Lennard-Jones fluid and the results compared with Adams' [1] at T*=1·15 and 1·25. The method generates equally reliable data using a much smaller number of molecules. Fluid states near a phase transition are simulated.
TL;DR: In this article, Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations, and the Kosterlitz-Thouless theory agrees well with the simulation results.
Abstract: Monte Carlo simulations of dislocation vector systems with long-range interactions reveal two possible types of phase transitions depending on the core energy of dislocations. For dislocations with a large core energy the melting transition is found to be continuous and due to dislocation unbinding. The Kosterlitz-Thouless theory agrees well with the simulation results. For a small core energy the melting transition is caused by the nucleation of grain boundary loops and is found to be first order. The latter transition may correspond to the previous computer experiments on various atomic systems. In addition to thermodynamic quantities such as the energy and specific heat, microscopic configurations and orientational correlation functions are also calculated.
TL;DR: In this paper, Monte Carlo statistical mechanics simulations have been carried out for liquid tetrahydrofuran (THF) with and without pseudorotation at 1 atm and 25 degrees C. The results are also compared with those from previous simulations of acyclic ethers.
Abstract: Monte Carlo statistical mechanics simulations have been carried out for liquid tetrahydrofuran (THF) with and without pseudorotation at 1 atm and 25 °C. The intermolecular potential functions consisted of Lennard‐Jones and Coulomb terms in the TIPS format reported previously for ethers. Pseudorotation of the ring was described using the generalized coordinates defined by Cremer and Pople, viz., the puckering amplitude and the phase angle of the ring. The corresponding intramolecular potential function was derived from molecular mechanics (MM2) calculations. Compared to the gas phase, the rings tend to be more flat and the population of the C2 twist geometry is slightly higher in liquid THF. However, pseudorotation has negligible effect on the calculated intermolecular structure and thermodynamic properties. The computed density, heat of vaporization, and heat capacity are in good agreement with experiment. The results are also compared with those from previous simulations of acyclic ethers. The present st...
TL;DR: In this article, the Monte Carlo method was used to predict the behavior of the lattice gas model for particular values of the D-D interactions, and it was shown that for repulsive first nearest-neighbour (V1) and second nearest neighbor (V2) interactions with V2=0.25 V1, the Monte-Carlo method gave similar results to those obtained by a cluster variation method calculation.
Abstract: In alpha ' Pd-D at low temperatures the deuterons become ordered on the octahedral sites of the Pd lattice due to D-D interactions. As this process does not measurably disrupt the palladium lattice the system provides an excellent approximation to a lattice gas. The Monte Carlo method of predicting the behaviour of the lattice gas model for particular values of the D-D interactions is described and it is shown that for repulsive first nearest-neighbour (V1) and second nearest-neighbour (V2) interactions with V2=0.25 V1, the Monte Carlo method gives similar results to those obtained by a cluster variation method calculation. However, the latter method only predicts the transition temperature accurately near stoichiometric compositions. The above choice of interactions also gives a good description of the real system for D concentrations between 64 and 68% and it is suggested how agreement at higher concentrations could be achieved by introducing longer range interactions. A method of estimating the values of Vn from diffuse neutron scattering above the transition temperature is also proposed.
TL;DR: In this article, the excess free energy and entropy of three water models (ST2, MCY and SPC) were determined using Monte Carlo thermodynamic integration, with soft spheres as a reference system.
Abstract: The excess free energy and entropy of three water models (ST2, MCY and SPC) are determined using Monte Carlo thermodynamic integration, with soft spheres as a reference system. The method used is compared with two other methods, the umbrella sampling and the overlap ratio methods. A simple self check for the umbrella sampling method is proposed.
TL;DR: In this article, a self consistent Monte Carlo particle model for simulation of semiconductor devices is presented, which is capable of correctly reproducing laboratory measurements and can be used as a design tool to evaluate novel ideas.
TL;DR: In this paper, the essential features of a Monte Carlo program which simulates the scattering and the retardation of energetic ions in amorphous targets are presented, and theoretical predictions obtained using the above expressions for nuclear scattering and electronic energy loss are shown to agree very well with experimental results.
Abstract: The essential features of a Monte Carlo program which simulates the scattering and the retardation of energetic ions in amorphous targets are presented. The new experimentally derived universal scattering cross-section of Kalbitzer and Oetzmann is used to describe nuclear scattering events. For electronic energy loss, the Lindhard-Scharff and Bethe formulae are used. The program was primarily developed to study the spatial distribution of ion deposited energy for lithographic applications. However, for initial verification, the program has been used to study the fundamental characteristics of ion transport for various ion-target combinations. The theoretical predictions obtained using the above expressions for nuclear scattering and electronic energy loss are shown to agree very well with experimental results.
TL;DR: In this paper, an exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described, for both one-dimensional and three-dimensional ferromagnetic and antiferromagnetic systems.
Abstract: An exact Monte Carlo method for calculating thermodynamic properties of quantum spin systems is described. Results for one-dimensional ferromagnetic and antiferromagnetic systems and for three-dimensional ferromagnetic systems show that the method can be used to study quantum spin systems as extensively as classical spin systems are studied with conventional Monte Carlo methods.
TL;DR: In this article, the authors used the grand canonical ensemble Monte Carlo method to simulate the behaviour of a marginally supercritical Lennard-Jones gas near a graphite surface, and the results reproduce the cusp-like shape of the experimentally observed adsorption isotherms.
Abstract: The grand canonical ensemble Monte Carlo method is used to simulate the behaviour of a marginally supercritical Lennard-Jones gas near a graphite surface. The results reproduce the cusp-like shape of the experimentally observed adsorption isotherms. Even at these high temperatures, the computations clearly show the occurrence of multilayer adsorption; up to four layers are discernible at sufficiently high pressures.
TL;DR: In this paper, a formalism was presented for estimating critical cluster size as defined in classical models for nucleation phenomena, which combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism.
Abstract: A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n2/3] is used to predict critical cluster size and critical supersaturation ratio, S*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.