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Computer simulation studies in condensed matter physics. Recent developments
Computer Physics Communications 56 (1989) 409—410 North-Holland
409
BOOK REVIEW Computer Simulation Studies in Condensed Matter Physics. Recent developments D.P. Landau, K.K. Mon and H.-B. SchUttler, eds., Springer Proceedings in Physics, vol. 33, Springer-Verlag, Berlin, 1988, 233 + IX pages. DM98.00 (hardcover). ISBN 3-540-50449-4.
Computer simulation is now the primary method for investigating the statistical mechanics of model physical systems. This volume contains the papers presented at a workshop held in Athens, Georgia, USA in February 1988. The two major sections cover classical (12 papers) and quantum (7 papers) systems; there is also a miscellaneous section of contributions (6 papers), and a single paper on computer graphics. In the space of a short review it is only possible to mention a few papers which particularly caught my eye. A long-standing problem in Monte Carlo simulations is the critical slowing down which takes place with standard Markov chain algorithms as the temperature approaches a critical value: the correlation time diverges to infinity and the computational efficiency tends to zero The physical ongin of this slowing down lies in the local updating in standard algorithms, and ~okal in the first paper of the collection reviews a number of multi-grid methods which have been introduced to improve the situation by introducing collective-mode updates into the algorithm. He concludes that the field is wide-open! Loh in his paper suggests that by coarsening the grid stochastically rather than deterministically it is possible to eliminate critical slowing down altogether. Challa and Hetherington discuss the use of a Gaussian ensemble in Monte Carlo. This puts the system in contact with a finite heat bath, and is intermediate between the canonical and microcanonical ensembles. The latter appears as one limit to the Gaussian ensemble and can be applied in this way to systems without equations of motions which cannot be studied by dynamic simulations. The main advantage of the method is that it enables a much easier discrimination between first- and second-order phase transitions than is possible with standard Metropolis canonical ensemble simulations. There are two papers on the important applications of simulation to polymer systems. Grest and Kremer consider the stochastic dynamics simulation of a model polymer with repulsive interaction between all pairs of monomers, with in addition attractive forces between neighbouring monomers. They show that this method can model dense as well as dilute systems, and they study in detail single star polymers and dense melts of chain polymers. In particular, they present the first unambiguous evidence from simulation of the correctness of the reptation model. Binder’s paper on Monte Carlo simulation of polymers is concerned with three topics: tests of the standard theory of phase separation in polymer mixtures, polymers in confined geometries, and polymers attached to walls. The use of molecular dynamics simulation in the realistic study of problems in materials science is reviewed by Landman. Some particular examples discussed are: the solid-melt interface in silicon, and liquid-phase epitaxial growth (driven by heat conduction out of the crystal-melt system); the growth of amorphous films by low-energy beam deposition; and solid-melt coexistence in finite alkali—halide clusters. In the case of metallic systems, new simulation methods have been introduced which take into account the density dependence of the effective pair potentials, and are applied to the melting of aluminium surfaces. 0010-4655/89/$03.50 © Elsevier Science Publishers By. (North-Holland)
410
Book review
Adsorption on surfaces is the topic of a paper by Abraham, which uses classical simulation to study krypton adsorbed on graphite, and path integral quantum simulation to study helium adsorbed on graphite. In the first case simulations of over a hundred thousand atoms show that the incommensurate phase consists of commensurate islands separated by an inter-connecting network of incommensurate domain walls, the structure of this network being a sensitive function of temperature and coverage. In the second case being a sensitive function of temperature and coverage. In the second case the simulations involve less than a hundred helium atoms, but this is sufficient to reveal a number of phases which are in agreement with the experimental phase diagram. In his second paper Landman uses the problem of electron attachment to ionic and hydrogen bonded clusters to illustrate two quantum mechanical methods: path integral molecular dynamics, and the time-dependent self-consistent field method, in which FFTs are used to integrate the time-dependent Schrodinger equation. In the latter case the calculations are made tractable by a mixed classical-quantum description. Benedek, Mi Woodward and Garner discuss recent developments in the application of Car—Parrinello methods in electronic structure calculation. Such methods are based on the density functional approach, but use a dynamical method to minimise the energy. They consider first-order equations of motions which give more rapid convergence than the original approach based on simulated annealing using the (second-order) molecular dynamics equation of motion. This is a fascinating book which contains a wealth of material. The articles are short and very condensed, but well written with good references. Doors are thereby opened to many interesting worlds. This book should be on every simulator’s bookshelf, or even desk. David FINCHAM Daresbury Laboratory
409
BOOK REVIEW Computer Simulation Studies in Condensed Matter Physics. Recent developments D.P. Landau, K.K. Mon and H.-B. SchUttler, eds., Springer Proceedings in Physics, vol. 33, Springer-Verlag, Berlin, 1988, 233 + IX pages. DM98.00 (hardcover). ISBN 3-540-50449-4.
Computer simulation is now the primary method for investigating the statistical mechanics of model physical systems. This volume contains the papers presented at a workshop held in Athens, Georgia, USA in February 1988. The two major sections cover classical (12 papers) and quantum (7 papers) systems; there is also a miscellaneous section of contributions (6 papers), and a single paper on computer graphics. In the space of a short review it is only possible to mention a few papers which particularly caught my eye. A long-standing problem in Monte Carlo simulations is the critical slowing down which takes place with standard Markov chain algorithms as the temperature approaches a critical value: the correlation time diverges to infinity and the computational efficiency tends to zero The physical ongin of this slowing down lies in the local updating in standard algorithms, and ~okal in the first paper of the collection reviews a number of multi-grid methods which have been introduced to improve the situation by introducing collective-mode updates into the algorithm. He concludes that the field is wide-open! Loh in his paper suggests that by coarsening the grid stochastically rather than deterministically it is possible to eliminate critical slowing down altogether. Challa and Hetherington discuss the use of a Gaussian ensemble in Monte Carlo. This puts the system in contact with a finite heat bath, and is intermediate between the canonical and microcanonical ensembles. The latter appears as one limit to the Gaussian ensemble and can be applied in this way to systems without equations of motions which cannot be studied by dynamic simulations. The main advantage of the method is that it enables a much easier discrimination between first- and second-order phase transitions than is possible with standard Metropolis canonical ensemble simulations. There are two papers on the important applications of simulation to polymer systems. Grest and Kremer consider the stochastic dynamics simulation of a model polymer with repulsive interaction between all pairs of monomers, with in addition attractive forces between neighbouring monomers. They show that this method can model dense as well as dilute systems, and they study in detail single star polymers and dense melts of chain polymers. In particular, they present the first unambiguous evidence from simulation of the correctness of the reptation model. Binder’s paper on Monte Carlo simulation of polymers is concerned with three topics: tests of the standard theory of phase separation in polymer mixtures, polymers in confined geometries, and polymers attached to walls. The use of molecular dynamics simulation in the realistic study of problems in materials science is reviewed by Landman. Some particular examples discussed are: the solid-melt interface in silicon, and liquid-phase epitaxial growth (driven by heat conduction out of the crystal-melt system); the growth of amorphous films by low-energy beam deposition; and solid-melt coexistence in finite alkali—halide clusters. In the case of metallic systems, new simulation methods have been introduced which take into account the density dependence of the effective pair potentials, and are applied to the melting of aluminium surfaces. 0010-4655/89/$03.50 © Elsevier Science Publishers By. (North-Holland)
410
Book review
Adsorption on surfaces is the topic of a paper by Abraham, which uses classical simulation to study krypton adsorbed on graphite, and path integral quantum simulation to study helium adsorbed on graphite. In the first case simulations of over a hundred thousand atoms show that the incommensurate phase consists of commensurate islands separated by an inter-connecting network of incommensurate domain walls, the structure of this network being a sensitive function of temperature and coverage. In the second case being a sensitive function of temperature and coverage. In the second case the simulations involve less than a hundred helium atoms, but this is sufficient to reveal a number of phases which are in agreement with the experimental phase diagram. In his second paper Landman uses the problem of electron attachment to ionic and hydrogen bonded clusters to illustrate two quantum mechanical methods: path integral molecular dynamics, and the time-dependent self-consistent field method, in which FFTs are used to integrate the time-dependent Schrodinger equation. In the latter case the calculations are made tractable by a mixed classical-quantum description. Benedek, Mi Woodward and Garner discuss recent developments in the application of Car—Parrinello methods in electronic structure calculation. Such methods are based on the density functional approach, but use a dynamical method to minimise the energy. They consider first-order equations of motions which give more rapid convergence than the original approach based on simulated annealing using the (second-order) molecular dynamics equation of motion. This is a fascinating book which contains a wealth of material. The articles are short and very condensed, but well written with good references. Doors are thereby opened to many interesting worlds. This book should be on every simulator’s bookshelf, or even desk. David FINCHAM Daresbury Laboratory