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El. knyga: Guide to Monte Carlo Simulations in Statistical Physics

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(University of Georgia), (Johannes Gutenberg Universität Mainz, Germany)
  • Formatas: PDF+DRM
  • Išleidimo metai: 10-Sep-2009
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511629754
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  • Formatas: PDF+DRM
  • Išleidimo metai: 10-Sep-2009
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511629754
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Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This edition now contains material describing powerful new algorithms that have appeared since the previous edition was published, and highlights recent technical advances and key applications that these algorithms now make possible. Updates also include several new sections and a chapter on the use of Monte Carlo simulations of biological molecules. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.

Expanding the topic of Monte Carlo simulation for graduate students and researchers in physics.

Recenzijos

Review of the first edition: 'This book will serve as a useful introduction to those entering the field, while for those already versed in the subject it provides a timely survey of what has been achieved.' D. C. Rapaport, Journal of Statistical Physics

Daugiau informacijos

This book expands the topic of Monte Carlo simulation for graduate students and researchers in physics.
Preface xiii
Introduction
1(6)
What is a Monte Carlo simulation?
1(1)
What problems can we solve with it?
2(1)
What difficulties will we encounter?
3(1)
Limited computer time and memory
3(1)
Statistical and other errors
3(1)
What strategy should we follow in approaching a problem?
4(1)
How do simulations relate to theory and experiment?
4(2)
Perspective
6(1)
References
6(1)
Some necessary background
7(41)
Thermodynamics and statistical mechanics: a quick reminder
7(21)
Basic notions
7(6)
Phase transitions
13(12)
Ergodicity and broken symmetry
25(1)
Fluctuations and the Ginzburg criterion
26(1)
A standard exercise: the ferromagnetic Ising model
27(1)
Probability theory
28(11)
Basic notions
28(2)
Special probability distributions and the central limit theorem
30(1)
Statistical errors
31(1)
Markov chains and master equations
32(2)
The `art' of random number generation
34(5)
Non-equilibrium and dynamics: some introductory comments
39(9)
Physical applications of master equations
39(2)
Conservation laws and their consequences
41(3)
Critical slowing down at phase transitions
44(1)
Transport coefficients
45(1)
Concluding comments
46(1)
References
46(2)
Simple sampling Monte Carlo methods
48(20)
Introduction
48(1)
Comparisons of methods for numerical integration of given functions
48(3)
Simple methods
48(2)
Intelligent methods
50(1)
Boundary value problems
51(2)
Simulation of radioactive decay
53(1)
Simulation of transport properties
54(2)
Neutron transport
54(1)
Fluid flow
55(1)
The percolation problem
56(4)
Site percolation
56(3)
Cluster counting: the Hoshen-Kopelman algorithm
59(1)
Other percolation models
60(1)
Finding the groundstate of a Hamiltonian
60(1)
Generation of `random' walks
61(5)
Introduction
61(1)
Random walks
62(1)
Self-avoiding walks
63(2)
Growing walks and other models
65(1)
Final remarks
66(2)
References
66(2)
Importance sampling Monte Carlo methods
68(70)
Introduction
68(1)
The simplest case: single spin-flip sampling for the simple Ising model
69(36)
Algorithm
70(4)
Boundary conditions
74(3)
Finite size effects
77(13)
Finite sampling time effects
90(8)
Critical relaxation
98(7)
Other discrete variable models
105(10)
Ising models with competing interactions
105(4)
q-state potts models
109(1)
Baxter and Baxter-Wu models
110(1)
Clock models
111(2)
Ising spin glass models
113(1)
Complex fluid models
114(1)
Spin-exchange sampling
115(5)
Constant magnetization simulations
115(1)
Phase separation
115(2)
Diffusion
117(3)
Hydrodynamic slowing down
120(1)
Microcanonical methods
120(2)
Demon algorithm
120(1)
Dynamic ensemble
121(1)
Q2R
121(1)
General remarks, choice of ensemble
122(1)
Statics and dynamics of polymer models on lattices
122(11)
Background
122(1)
Fixed bond length methods
123(2)
Bond fluctuation method
125(1)
Enhanced sampling using a fourth dimension
126(1)
The `wormhole algorithm' - another method to equilibrate dense polymeric systems
127(1)
Polymers in solutions of variable quality: θ-point, collapse transition, unmixing
128(2)
Equilibrium polymers: a case study
130(3)
Some advice
133(5)
References
134(4)
More on importance sampling Monte Carlo methods for lattice systems
138(59)
Cluster flipping methods
138(7)
Fortuin-Kasteleyn theorem
138(1)
Swendsen-Wang method
139(3)
Wolff method
142(1)
`Improved estimators'
143(1)
Invaded cluster algorithm
143(1)
Probability changing cluster algorithm
144(1)
Specialized computational techniques
145(6)
Expanded ensemble methods
145(1)
Multispin coding
145(1)
N-fold way and extensions
146(3)
Hybrid algorithms
149(1)
Multigrid algorithms
149(1)
Monte Carlo on vector computers
149(1)
Monte Carlo on parallel computers
150(1)
Classical spin models
151(9)
Introduction
151(1)
Simple spin-flip method
152(2)
Heatbath method
154(1)
Low temperature techniques
155(1)
Over-relaxation methods
155(1)
Wolff embedding trick and cluster flipping
156(1)
Hybrid methods
157(1)
Monte Carlo dynamics vs. equation of motion dynamics
157(1)
Topological excitations and solitons
158(2)
System with quenched rendomness
160(13)
General comments: averaging in random systems
160(5)
Parallel tempering: a general method to better equilibrate systems with complex energy landscapes
165(1)
Random fields and random bonds
165(1)
Spin glasses and optimization by simulated annealing
166(5)
Ageing in spin glasses and related systems
171(1)
Vector spin glasses: developments and surprises
172(1)
Models with mixed degress of freedom: Si/Ge alloys, a case study
173(1)
Sampling the free energy and entropy
174(4)
Thermodynamic integration
174(2)
Groundstate free energy determination
176(1)
Estimation of intensive variables: the chemical potential
177(1)
Lee-Kosterlitz method
177(1)
Free energy from finite size dependence at Tc
178(1)
Miscellaneous topics
178(15)
Inhomogeneous systems: surfaces, interfaces, etc.
178(6)
Other Monte Carlo schemes
184(2)
Inverse and reverse Monte Carlo methods
186(1)
Finite size effects: a review and summary
187(1)
More about error estimation
188(2)
Random number generators revisited
190(3)
Summary and perspective
193(4)
References
193(4)
Off-lattice models
197(60)
Fluids
197(28)
NVT ensemble and the virial theorem
197(3)
NpT ensemble
200(4)
Grand canonical ensemble
204(4)
Near critical coexistence: a case study
208(2)
Subsystems: a case study
210(5)
Gibbs ensemble
215(3)
Widom particle insertion method and variants
218(2)
Monte Carlo Phase Switch
220(4)
Cluster algorithm for fluids
224(1)
`Short range' interactions
225(1)
Cutoffs
225(1)
Verlet tables and cell structure
225(1)
Minimum image convention
226(1)
Mixed degrees of freedom reconsidered
226(1)
Treatment of long range forces
226(3)
Reaction field method
226(1)
Ewald method
226(2)
Fast multipole method
228(1)
Adsorbed monolayers
229(2)
Smooth substrates
229(1)
Periodic substrate potentials
229(2)
Complex fluids
231(3)
Application of the Liu-Luijten algorithm to a binary fluid mixture
233(1)
Polymers: an introduction
234(16)
Length scales and models
234(7)
Asymmetric polymer mixtures: a case study
241(4)
Applications: dynamics of polymer melts; thin adsorbed polymeric films
245(3)
Polymer melts: speeding up bond fluctuation model simulations
248(2)
Configurational bias and `smart Monte Carlo'
250(3)
Outlook
253(4)
References
253(4)
Reweighting methods
257(28)
Background
257(3)
Distribution functions
257(1)
Umbrella sampling
257(3)
Single histogram method: the Ising model as a case study
260(7)
Multihistogram method
267(1)
Broad histogram method
268(1)
Transition matrix Monte Carlo
268(1)
Multicanonical sampling
269(5)
The multicanonical approach and its relationship to canonical sampling
269(1)
Near first order transitions
270(2)
Groundstates in complicated energy landscapes
272(1)
Interface free energy estimation
273(1)
A case study: the Casimir effect in critical systems
274(2)
`Wang-Landau sampling'
276(5)
Basic algorithm
276(3)
Applications to models with continuous variables
279(1)
Case studies with two-dimensional Wang-Landau sampling
279(1)
Back to numerical integration
279(2)
A case study: evaporation/condensation transition of droplets
281(4)
References
282(3)
Quantum Monte Carlo methods
285(39)
Introduction
285(2)
Feynman path integral formulation
287(10)
Off-lattice problems: low-temperature properties of crystals
287(6)
Bose statistics and superfluidity
293(1)
Pat integral formulation for rotational degrees of freedom
294(3)
Lattice problems
297(19)
The Ising model in a transverse field
297(1)
Anisotropic Heisenberg chain
298(4)
Fermions on a lattice
302(2)
An intermezzo: the minus sign problem
304(2)
Spinless fermions revisited
306(4)
Cluster methods for quantum lattice models
310(1)
Continuous time simulations
310(1)
Decoupled cell method
311(1)
Handscomb's method
312(1)
Wang-Landau sampling for quantum models
313(1)
Fermion determinants
314(2)
Monte Carlo methods for the study of groundstate properties
316(4)
Variational Monte Carlo (VMC)
316(2)
Green's function Monte Carlo methods (GFMC)
318(2)
Concluding remarks
320(4)
References
321(3)
Monte Carlo renormalization group methods
324(14)
Introduction to renormalization group theory
324(4)
Real space renormalization group
328(1)
Monte Carlo renormalization group
329(9)
Large cell renormalization
329(2)
Ma's method: finding critical exponents and the fixed point Hamiltonian
331(1)
Swendsen's method
332(2)
Location of phase boundaries
334(1)
Dynamic problems: matching time-dependent correlation functions
335(1)
Inverse Monte Carlo renormalization group transformations
336(1)
References
336(2)
Non-equilibrium and irreversible processes
338(27)
Introduction and perspective
338(1)
Driven diffusive systems (driven lattice gases)
338(3)
Crystal growth
341(3)
Domain growth
344(3)
Polymer growth
347(2)
Linear polymers
347(1)
Gelation
347(2)
Growth of structures and patterns
349(4)
Eden model of cluster growth
349(1)
Diffusion limited aggregation
349(3)
Cluster-cluster aggregation
352(1)
Cellular automata
352(1)
Models for film growth
353(5)
Background
353(1)
Ballistic deposition
354(1)
Sedimentation
355(1)
Kinetic Monte Carlo and MBE growth
356(2)
Transition path sampling
358(1)
Forced polymer pore translocation: a case study
359(3)
Outlook: variations on a theme
362(3)
References
362(3)
Lattice gauge models: a brief introduction
365(14)
Introduction: gauge invariance and lattice gauge theory
365(2)
Some technical matters
367(1)
Results for Z(N) lattice gauge models
367(1)
Compact U(1) gauge theory
368(1)
SU(2) lattice gauge theory
369(1)
Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter
370(2)
The deconfinement transition of QCD
372(3)
Towards quantitative predictions
375(4)
References
377(2)
A brief review of other methods of computer simulation
379(22)
Introduction
379(1)
Molecular dynamics
379(9)
Integration methods (microcanonical ensemble)
379(4)
Other ensembles (constant temperature, constant pressure, etc.)
383(3)
Non-equilibrium molecular dynamics
386(1)
Hybrid methods (MD + MC)
386(1)
Ab initio molecular dynamics
387(1)
Hyperdynamics and metadynamics
388(1)
Quasi-classical spin dynamics
388(4)
Langevin equations and variations (cell dynamics)
392(1)
Micromagnetics
393(1)
Dissipative particle dynamics (DPD)
393(2)
Lattice gas cellular automata
395(1)
Lattice Boltzmann equation
395(1)
Multiscale simulation
396(5)
References
398(3)
Monte Carlo simulations at the periphery of physics and beyond
401(18)
Commentary
401(1)
Astrophysics
401(1)
Materials science
402(1)
Chemistry
403(2)
`Biological inspired' physics
405(4)
Commentary and perspective
405(1)
Lattice proteins
406(1)
Cell sorting
407(2)
Biology
409(1)
Mathematics/statistics
410(1)
Sociophysics
410(1)
Econophysics
411(1)
`Traffic' simulations
412(1)
Medicine
413(1)
Networks: what connections really matter?
414(1)
Finance
415(4)
References
416(3)
Monte Carlo studies of biological molecules
419(11)
Introduction
419(1)
Protein folding
420(6)
Introduction
420(1)
How to best simulate proteins: Monte Carlo or molecular dynamics
421(1)
Generalized ensemble methods
421(2)
Globular proteins: a case study
423(1)
Simulations of membrane proteins
424(2)
Monte Carlo simulations of carbohydrates
426(1)
Determining macromolecular structures
427(1)
Outlook
428(2)
References
428(2)
Outlook
430(3)
Appendix: listing of programs mentioned in the text 433(32)
Index 465
David P. Landau received a BA in Physics from Princeton University in 1963 and a Ph.D. in experimental Physics from Yale University in 1967. After doing postdoctoral research at the CNRS in Grenoble, France and teaching at Yale for a year he moved to the University of Georgia where he initiated a research program of Monte Carlo studies in statistical physics. He is currently the Distinguished Research Professor of Physics and founding Director of the Center for Simulational Physics at the University of Georgia. He has been teaching graduate courses in computer simulations since 1982. He has authored/co-authored more than 370 research publications and edited/co-edited more than 20 books. David Landau is a Fellow of the American Physical Society and a past Chair of the Division of Computational Physics of the APS. He received the Jesse W. Beams award from SESAPS as well as Humboldt Fellowship and Humboldt Senior US Scientist awards. The University of Georgia named him a Senior Teaching Fellow in 1993. In 1998 he also became Adjunct Professor at the Helsinki University of Technology. In 1999 he was named a Fellow of the Japan Society for the Promotion of Science. In 2002 he received the Aneesur Rahman Prize for Computational Physics from the APS, and in 2003 the Lamar Dodd Award for Creative Research from the University of Georgia. In 2005 he became the Senior Guanbiao Distinguished Professor (Visiting) at Zhejiang U. in China. In 2007 he received the Nicholson Medal for Human Outreach from the APS. He is currently a Principal Editor for the journal Computer Physics Communications. Kurt Binder received his Ph.D. in 1969 at the Technical University of Vienna. His thesis dealt with Monte Carlo simulations of Ising and Heisenberg magnets, and since then he has pioneered the development of Monte Carlo simulation methods in statistical physics. From 1969 until 1974 Kurt Binder worked at the Technical University in Munich, interrupted by a stay as IBM postdoctoral fellow in Zurich in 19723. After a year at Bell Laboratories in Murray Hill, NJ (1974) and a first appointment as Professor of Theoretical Physics at the University of Saarbrücken back in Germany (19747), he was awarded a joint appointment as Full Professor at the University of Cologne and as one of the Directors of the Institute of Solid State Research at Jülich (197783). He has held his present position as Professor of Theoretical Physics at the University of Mainz, Germany, since 1983, and since 1989 he has also been an external member of the Max-Planck-Institut for Polymer Research at Mainz. Kurt Binder has authored/co-authored more than 900 research publications and edited 5 books dealing with computer simulations. Kurt Binder received the Max Planck Medal of the German Physical Society in 1993. He also acts as Editorial Board member of several journals and has served as Chairman of the IUPAP Commission on Statistical Physics. In 2001 he was awarded the Berni Alder CECAM prize from the European Physical Society. In 2007 he received the Boltzmann Medal from the International Union of Pure and Applied Physics, and was named one of the first Gutenberg Fellows at the University of Mainz.