Computer Simulation Studies in Condensed Matter Physics: Recent Developments Proceeding of the Workshop, Athens, GA, USA, February 15–26, 1988

243 Pages·1988·7.626 MB·English

by  D. P. Landau, K. K. Mon, H.-B. Schüttler (auth.), Professor David P. Landau Ph.D., Professor K. K. Mon Ph.D., Professor Heinz-Bernd Schüttler Ph.D. (eds.)

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Springer Proceedings in Physics
Managing Editor: H. K. V. Lotsch
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Volume 32 Universalities in Condensed Matter
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Volume 33 Computer Simulation Studies in Condensed
Matter Physics: Recent Developments
Editors: D. P. Landau, K. K. Mon, and H.-B. Schuttler
Volumes 1 - 29 are listed on the back inside cover
Computer Simulation
Studies in
Condensed Matter Physics
Recent Developments
Proceedings of the Workshop,
Athens, GA, USA, February 15-26, 1988
Editors: D. P. Landau, K. K. Mon,
and H.-B. Schuttler
With 101 Figures
Springer-Verlag Berlin Heidelberg New York
London Paris Tokyo
Professor David P. Landau, Ph. D.
Professor K. K. Mon, Ph. D.
Professor Heinz-Bernd Schuttler, Ph. D.
Center for Simulational Physics, The University of Georgia, Athens, GA 30602, USA
ISBN-13: 978-3-642-93402-5 e-ISBN-13: 978-3-642-93400-1
001: 10.1007/978-3-642-93400-1
Library of Congress Cataloging-in-Publication Data. Computer simulation studies in condensed matter
physics: recent developments: proceedings of the workshop. Athens, GA, USA, February 15-26, 1988/
editors, D. P. Landau, K. K. Mon, and H.-B. Schuttler. (Springer proceedings in physics; v. 33) Includes
index.
(U.S.: alk. paper)
1. Condensed matter - Computer simulation - Congresses. I. Landau, David P. II. Mon, K. K. (Kin K.),
1950-. III. Schuttler, Heinz-Bernd, 1956-. IV. Series. QC173.4.C65C65 1988 530.4'1-dc 19 88-30707
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Preface
Computer simulation studies in condensed matter physics represent a rapidly
changing field, making significant contributions in techniques and in new results to
important physical problems. The workshop on "Recent Developments in Com
puter Simulation Studies in Condensed Matter Physics", held at the Center for
Simulational Physics at the University of Georgia, February 14-26, 1988, was an
attempt to bring together some of the practitioners in this field and to provide a
forum for the presentation and exchange of new ideas and recent developments.
These proceedings are a record of the workshop and are published with the goal
of timely dissemination of the papers to a wider audience.
Although by their very nature workshops are limited in their scope of coverage,
a broad range of current topics is discussed. The papers present new techniques
and results on both static and dynamical phenomena of classical and quantum
mechanical systems. The reader will find descriptions of studies of static properties
as well as time-dependent ones where time may be real time, stochastic time or
imaginary (path integral) time.
A substantial portion of the material, the first part of the proceedings, deals with
simulations of classical systems. Monte Carlo simulations are presented for simple
Ising models. On the one hand, the reader will find here new approaches suggested
for avoiding critical slowing down, and on the other, there are descriptions of the
study of critical slowing down using standard techniques. Both standard and
novel Monte Carlo methods have been used to study static properties at phase
transitions. New results for classical spin dynamics are discussed. New material
is presented for the formation of aggregates. Molecular dynamics and/or Monte
Carlo approaches have been developed for studying fluid flow as well as for
polymer systems, adsorbed monolayers and crystal growth.
The second part of the proceedings is devoted to the simulation of quantum
systems. New results for interacting boson and fermion systems, adsorbed 4He
monolayers and the electronic structure of clusters have been obtained by numer
ical functional and path integral techniques. Novel variational wave functions
and minimization techniques are discussed in the context of solid 4He, and the
electronic structure of real atoms and solids. Promising new hybrid methods
have been developed by combining more conventional quantum methods, such as
quantum Monte Carlo or density functional theory, with well-established classi
cal techniques, such as molecular dynamics. The workshop also included several
presentations about emerging computer technologies and programming methods.
but for the most part no written record is available.
v
We hope that the readers will benefit from papers in their own special field as
well as gain new ideas from other related specialties.
This workshop was made possible through the generous support of the Ad
vanced Computational Methods Center, the Department of Physics and Astronomy,
and the Vice President for Research at the University of Georgia.
Athens, GA, USA D.P. Landau
April 1988 KK Man
H.-B. Schuttler
VI
Contents
Introduction
By D.P. Landau, K.K. Mon, and H.-B. Schuttler 1
Part I Classical Systems
New Numerical Algorithms for Critical Phenomena (Multi-Grid Methods
and All That)
By A.D. Sokal ........................................ 6
Multigrid Monte Carlo Methods
By E. Loh, Jr. (With 1 Figure) ................. . . . . . . . . . . . . 19
Monte Carlo Simulations Using the Gaussian Ensemble
By M.S.S. Challa and J.H. Hetherington (With 7 Figures) . . . . . . . . . . . 31
Classical Spin Dynamics in the Two-Dimensional Anisotropic Heisenberg
Model
By G.M. Wysin, M.E. Gouvea, A.R. Bishop, and F.G. Mertens
(With 6 Figures) .............................. . . . . . . . . . 40
Simulation Study of Light Scattering from Soot Agglomerates
By R.D. Mountain (With 4 Figures) ......................... 49
Simulation of Non-equilibrium Growth and Aggregation Processes
By P. Meakin (With 9 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Growth by Gradients: Fractal Growth and Pattern Formation in a
Laplacian Field
By F. Family (With 6 Figures) ............................. 65
Dynamics of Dense Polymers: A Molecular Dynamics Approach
By G.S. Grest and K. Kremer (With 5 Figures) ...... . . . . . . . . . . . . 76
Monte Carlo Simulations of Polymer Systems
By K. Binder (With 9 Figures) ............................. 84
Molecular Dynamics: A New Approach to Hydrodynamics?
By D.C. Rapaport (With 5 Figures) .......................... 98
Molecular Dynamics Simulations in Material Science and Condensed
Matter Physics
By U. Landman (With 8 Figures) ........................... 108
VII
Simulations of Oxygen Monolayer and Bilayer Systems
By K.M. Flurchick and R.D. Etters (With 3 Figures) .............. 124
Part II Quantum Systems
Classical and Quantum Simulations of Quasi Two-Dimensional Condensed
Phases: Krypton and Helium on Graphite
By F.F. Abraham (With 7 Figures) .......................... 134
Path-Integral and Real-Time Dynamics Simulations of Quantum Systems
By U. Landman (With 5 Figures) ........................... 144
Superfluidity of a Two-Dimensional Bose-Coulomb Gas
By D. Peters and B. Alder (With 3 Figures) .................... 157
Quantum Monte Carlo Studies of the Holstein Model
By R.T. Scalettar, N.E. Bickers, and D.J. Scalapino (With 2 Figures) 166
Structure of the Wave Function of Crystalline 4He
By S.A. Vitiello, KJ. Runge, and M.H. Kalos (With 3 Figures) . . . . . .. 172
Electronic Structure Calculation by Nonlinear Optimization: Application to
Metals
By R. Benedek, B.I. Min, C. Woodward, and J. Garner (With 2 Figures) 179
A Method for Determining Many Body Wavefunctions
By C.J. Umrigar, K.G. Wilson, and J.W. Wilkins (With 1 Figure) 185
Part III Computer Graphics
Computer Graphics for Scientists and Engineers
By S. Follin (With 4 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 196
Part IV Contributed Papers
Monte Carlo Calculation of Transfer Matrix Eigenvalues
By M.P. Nightingale and R.G. Caflisch ....................... 208
Finite Size Effects at First-Order Phase Transitions Revisited
By P. Peczak and D.P. Landau (With 1 Figure) ................ " 214
Correlation Time Measurements for the d=2 Ising Model
By A.M. Ferrenberg and R.H. Swendsen (With 2 Figures) .......... 217
Monte Carlo Study of the Critical Dynamics at the Surface of an Ising
Model
By P.A. Slotte, S. Wansleben, and D.P. Landau (With 1 Figure) ...... 222
A New Model of Interactive Percolation
By S.R. Anderson and F. Family (With 4 Figures) . . . . . . . . . . . . . . .. 225
VIII
MD Simulation of 2D Rb Liquid and Solid Phases in Graphite
By J.D. Fan, O.A. Karim, G. Reiter, and S.C. Moss (With 3 Figures) 229
Index of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 233
IX
Introduction
D.P. Landau, K.K. Mon, and H.-B. Schuttler
Center for Simulational Physics, University of Georgia, Athens, GA 30602, USA
Computer simulations have become recognized as a new approach to research in
physics; they provide great flexibility in the choice of parameters to be included, the
ensemble to be used, and even the questions to be answered. Simulations provide not only
numerical data but also allow the visualization of microscopic behavior (through graphics
output) which helps flesh out our intuitive understanding of the processes at work. Early
work was done using computers which were considerably slower than today's personal
computers, and it was only in the late 1960's that computer speed had increased to the
point that detailed studies of physical problems became possible. A broad range of
problems which have already been attacked using Monte Carlo methods has been
summarized in two earlier volumes in the Springer-Verlag series on Topics in Current
Physics and we refer the newcomer to the field to these books [1, 2]. The proceedings of
this workshop concentrate instead on the most recent developments in the field of
computer simulations in condensed matter physics.
Monte Carlo methods determine the properties of interacting many-particle systems
by generating (carefully chosen) sample configurations of the system and using these states
to estimate the actual distribution of the total number of states. New configurations are
generated from precedinp; ones using "single site" changes, but "multi-spin" methods may
speed up the computation substantially either through the implementation of vector
operations or through modification of the fundamental dynamic time scale. Increasing
accuracy is of course obtainable by simply using larger systems and generating more states.
A "standard" unit for measuring the lengths of Monte Carlo runs is the MCS/site or Monte
Carlo Step per site, which represents one examination of every site in the system. Whereas
two decades ago only a few hundred MCS/site were generally possible for classical systems,
today run lengths for simple models may he measured in millions of MCS/site. The speed
of modern computers has also made it possible to examine more realistic models, which of
course consume far more computer time than do simple theoretical systems. In these
proceedings you will find data obtained using both Cyber 205 and CRA Y /XMP
supercomputers; on the other hand there are also very high resolution data for simple,
small systems which have been produced by using a totally dedicated micro-Vax.
Whereas Monte Carlo methods may be applied directly to collections of classical
particles, they may be used only indirectly for the exploration of quantum systems.
Quantum behavior can be produced only with the inclusion of an extra degree of freedom
(or added dimension) before simulations are introduced and the second part of these
proceedings presents some novel ways in which this may be done.
A second simulation approach, Molecular Dynamics, involves the integration of
coupled equations of motion which govern the time development of classical systems. The
resultant (true) dynamics is different than the (stochastic) kinetic behaviot resulting from
Monte Carlo simulations although it is presently possible to extend such studies to only
very short periods of physical time.In these proceedings the reader will find descriptions of
the application of molecular dynamics techniques to larger and to more complex collections
of interacting particles than is usually found in the literature.
The representaion of simulations data through computer graphics is gaining in importance
and the state of the art in computer graphics is discussed in these proceedings by Follin.
Springer Proceedings in Physics Vol. 33: Computer Simulation Studies in Condensed Matter Physics
Editors: D. P. Landau· K. K. Mon· H-B. Schiittler © Springer-Verlag Berlin Heidelberg 1988