Atnaujinkite slapukų nuostatas

Guide to Monte Carlo Simulations in Statistical Physics 4th Revised edition [Kietas viršelis]

3.80/5 (10 ratings by Goodreads)
(University of Georgia), (Johannes Gutenberg Universität Mainz, Germany)
  • Formatas: Hardback, 538 pages, aukštis x plotis x storis: 253x180x28 mm, weight: 1200 g, 172 Line drawings, unspecified
  • Išleidimo metai: 13-Nov-2014
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107074029
  • ISBN-13: 9781107074026
Kitos knygos pagal šią temą:
Guide to Monte Carlo Simulations in Statistical Physics 4th Revised editionDidesnis paveikslėlis
  • Formatas: Hardback, 538 pages, aukštis x plotis x storis: 253x180x28 mm, weight: 1200 g, 172 Line drawings, unspecified
  • Išleidimo metai: 13-Nov-2014
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107074029
  • ISBN-13: 9781107074026
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781107074026.html
Raktažodžiai:
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 fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. 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.

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 revised fourth edition provides an introduction to computer simulations in physics, cutting-edge algorithms, essential techniques, and petascale computing.
Preface xv
1 Introduction
1(6)
1.1 What is a Monte Carlo simulation?
1(1)
1.2 What problems can we solve with it?
2(1)
1.3 What difficulties will we encounter?
3(1)
1.3.1 Limited computer time and memory
3(1)
1.3.2 Statistical and other errors
3(1)
1.4 What strategy should we follow in approaching a problem?
4(1)
1.5 How do simulations relate to theory and experiment?
4(1)
1.6 Perspective
5(2)
References
6(1)
2 Some necessary background
7(44)
2.1 Thermodynamics and statistical mechanics: a quick reminder
7(23)
2.1.1 Basic notions
7(8)
2.1.2 Phase transitions
15(12)
2.1.3 Ergodicity and broken symmetry
27(1)
2.1.4 Fluctuations and the Ginzburg criterion
27(1)
2.1.5 A standard exercise: the ferromagnetic Ising model
28(2)
2.2 Probability theory
30(11)
2.2.1 Basic notions
30(1)
2.2.2 Special probability distributions and the central limit theorem
31(2)
2.2.3 Statistical errors
33(1)
2.2.4 Markov chains and master equations
33(2)
2.2.5 The `art' of random number generation
35(6)
2.3 Non-equilibrium and dynamics: some introductory comments
41(10)
2.3.1 Physical applications of master equations
41(2)
2.3.2 Conservation laws and their consequences
43(3)
2.3.3 Critical slowing down at phase transitions
46(2)
2.3.4 Transport coefficients
48(1)
2.3.5 Concluding comments: why bother about dynamics when doing Monte Carlo for statics?
48(1)
References
48(3)
3 Simple sampling Monte Carlo methods
51(20)
3.1 Introduction
51(1)
3.2 Comparisons of methods for numerical integration of given functions
51(3)
3.2.1 Simple methods
51(2)
3.2.2 Intelligent methods
53(1)
3.3 Boundary value problems
54(2)
3.4 Simulation of radioactive decay
56(1)
3.5 Simulation of transport properties
57(1)
3.5.1 Neutron transport
57(1)
3.5.2 Fluid flow
58(1)
3.6 The percolation problem
58(5)
3.6.1 Site percolation
59(3)
3.6.2 Cluster counting: the Hoshen--Kopelman algorithm
62(1)
3.6.3 Other percolation models
63(1)
3.7 Finding the groundstate of a Hamiltonian
63(1)
3.8 Generation of `random' walks
64(5)
3.8.1 Introduction
64(1)
3.8.2 Random walks
65(1)
3.8.3 Self-avoiding walks
66(2)
3.8.4 Growing walks and other models
68(1)
3.9 Final remarks
69(2)
References
69(2)
4 Importance sampling Monte Carlo methods
71(73)
4.1 Introduction
71(1)
4.2 The simplest case: single spin-flip sampling for the simple Ising model
72(36)
4.2.1 Algorithm
73(3)
4.2.2 Boundary conditions
76(3)
4.2.3 Finite size effects
79(14)
4.2.4 Finite sampling time effects
93(7)
4.2.5 Critical relaxation
100(8)
4.3 Other discrete variable models
108(9)
4.3.1 Ising models with competing interactions
108(4)
4.3.2 q-state Potts models
112(1)
4.3.3 Baxter and Baxter--Wu models
113(1)
4.3.4 Clock models
114(1)
4.3.5 Ising spin glass models
115(1)
4.3.6 Complex fluid models
116(1)
4.4 Spin--exchange sampling
117(6)
4.4.1 Constant magnetization simulations
117(1)
4.4.2 Phase separation
118(2)
4.4.3 Diffusion
120(2)
4.4.4 Hydrodynamic slowing down
122(1)
4.5 Microcanonical methods
123(1)
4.5.1 Demon algorithm
123(1)
4.5.2 Dynamic ensemble
123(1)
4.5.3 Q2R
124(1)
4.6 General remarks, choice of ensemble
124(2)
4.7 Statics and dynamics of polymer models on lattices
126(13)
4.7.1 Background
126(1)
4.7.2 Fixed bond length methods
126(2)
4.7.3 Bond fluctuation method
128(1)
4.7.4 Enhanced sampling using a fourth dimension
128(2)
4.7.5 The `wormhole algorithm' -- another method to equilibrate dense polymeric systems
130(1)
4.7.6 Polymers in solutions of variable quality: θ-point, collapse transition, unmixing
130(3)
4.7.7 Equilibrium polymers: a case study
133(3)
4.7.8 The pruned enriched Rosenbluth method (PERM): a biased sampling approach to simulate very long isolated chains
136(3)
4.8 Some advice
139(5)
References
140(4)
5 More on importance sampling Monte Carlo methods for lattice systems
144(68)
5.1 Cluster flipping methods
144(7)
5.1.1 Fortuin--Kasteleyn theorem
144(1)
5.1.2 Swendsen--Wang method
145(3)
5.1.3 Wolff method
148(1)
5.1.4 Improved estimators'
149(1)
5.1.5 Invaded cluster algorithm
149(1)
5.1.6 Probability changing cluster algorithm
150(1)
5.2 Specialized computational techniques
151(6)
5.2.1 Expanded ensemble methods
151(1)
5.2.2 Multispin coding
151(1)
5.2.3 N--fold way and extensions
152(3)
5.2.4 Hybrid algorithms
155(1)
5.2.5 Multigrid algorithms
155(1)
5.2.6 Monte Carlo on vector computers
155(1)
5.2.7 Monte Carlo on parallel computers
156(1)
5.3 Classical spin models
157(9)
5.3.1 Introduction
157(1)
5.3.2 Simple spin--flip method
158(2)
5.3.3 Heatbath method
160(1)
5.3.4 Low temperature techniques
161(1)
5.3.5 Over-relaxation methods
161(1)
5.3.6 Wolff embedding trick and cluster flipping
162(1)
5.3.7 Hybrid methods
163(1)
5.3.8 Monte Carlo dynamics vs. equation of motion dynamics
163(1)
5.3.9 Topological excitations and solitons
164(2)
5.4 Systems with quenched randomness
166(13)
5.4.1 General comments: averaging in random systems
166(5)
5.4.2 Parallel tempering: a general method to better equilibrate systems with complex energy landscapes
171(1)
5.4.3 Random fields and random bonds
172(1)
5.4.4 Spin glasses and optimization by simulated annealing
173(5)
5.4.5 Ageing in spin glasses and related systems
178(1)
5.4.6 Vector spin glasses: developments and surprises
178(1)
5.5 Models with mixed degrees of freedom: Si/Ge alloys, a case study
179(2)
5.6 Methods for systems with long range interactions
181(2)
5.7 Parallel tempering, simulated tempering, and related methods: accuracy considerations
183(3)
5.8 Sampling the free energy and entropy
186(4)
5.8.1 Thermodynamic integration
186(1)
5.8.2 Groundstate free energy determination
187(1)
5.8.3 Estimation of intensive variables: the chemical potential
188(1)
5.8.4 Lee--Kosterlitz method
189(1)
5.8.5 Free energy from finite size dependence at Tc
189(1)
5.9 Miscellaneous topics
190(17)
5.9.1 Inhomogeneous systems: surfaces, interfaces, etc.
190(6)
5.9.2 Anisotropic critical phenomena: simulation boxes with arbitrary aspect ratio
196(2)
5.9.3 Other Monte Carlo schemes
198(2)
5.9.4 Inverse and reverse Monte Carlo methods
200(2)
5.9.5 Finite size effects: review and summary
202(1)
5.9.6 More about error estimation
202(2)
5.9.7 Random number generators revisited
204(3)
5.10 Summary and perspective
207(5)
References
208(4)
6 Off-lattice models
212(70)
6.1 Fluids
212(30)
6.1.1 NVT ensemble and the virial theorem
212(4)
6.1.2 NpT ensemble
216(4)
6.1.3 Grand canonical ensemble
220(4)
6.1.4 Near critical coexistence: a case study
224(2)
6.1.5 Subsystems: a case study
226(5)
6.1.6 Gibbs ensemble
231(3)
6.1.7 Widom particle insertion method and variants
234(2)
6.1.8 Monte Carlo phase switch
236(3)
6.1.9 Cluster algorithm for fluids
239(2)
6.1.10 Event chain algorithms
241(1)
6.2 `Short range' interactions
242(1)
6.2.1 Cutoffs
242(1)
6.2.2 Verlet tables and cell structure
242(1)
6.2.3 Minimum image convention
243(1)
6.2.4 Mixed degrees of freedom reconsidered
243(1)
6.3 Treatment of long range forces
243(3)
6.3.1 Reaction field method
243(1)
6.3.2 Ewald method
244(1)
6.3.3 Fast multipole method
245(1)
6.4 Adsorbed monolayers
246(1)
6.4.1 Smooth substrates
246(1)
6.4.2 Periodic substrate potentials
246(1)
6.5 Complex fluids
247(4)
6.5.1 Application of the Liu--Luijten algorithm to a binary fluid mixture
250(1)
6.6 Polymers: an introduction
251(16)
6.6.1 Length scales and models
251(6)
6.6.2 Asymmetric polymer mixtures: a case study
257(4)
6.6.3 Applications: dynamics of polymer melts; thin adsorbed polymeric films
261(4)
6.6.4 Polymer melts: speeding up bond fluctuation model simulations
265(2)
6.7 Configurational bias and `smart Monte Carlo'
267(3)
6.8 Estimation of excess free energies due to walls for fluids and solids
270(2)
6.9 A symmetric, Lennard--Jones mixture: a case study
272(3)
6.10 Finite size effects on interfacial properties: a case study
275(2)
6.11 Outlook
277(5)
References
278(4)
7 Reweighting methods
282(37)
7.1 Background
282(3)
7.1.1 Distribution functions
282(1)
7.1.2 Umbrella sampling
282(3)
7.2 Single histogram method
285(10)
7.2.1 The Ising model as a case study
286(6)
7.2.2 The surface--bulk multicritical point: another case study
292(3)
7.3 Multihistogram method
295(1)
7.4 Broad histogram method
296(1)
7.5 Transition matrix Monte Carlo
296(1)
7.6 Multicanonical sampling
297(5)
7.6.1 The multicanonical approach and its relationship to canonical sampling
297(2)
7.6.2 Near first order transitions
299(1)
7.6.3 Groundstates in complicated energy landscapes
300(1)
7.6.4 Interface free energy estimation
301(1)
7.7 A case study: the Casimir effect in critical systems
302(1)
7.8 Wang--Landau sampling
303(11)
7.8.1 Basic algorithm
303(4)
7.8.2 Applications to models with continuous variables
307(1)
7.8.3 A simple example of two-dimensional Wang--Landau sampling
307(1)
7.8.4 Microcanonical entropy inflection points
308(1)
7.8.5 Back to numerical integration
309(1)
7.8.6 Replica exchange Wang--Landau sampling
310(4)
7.9 A case study: evaporation/condensation transition of droplets
314(5)
References
316(3)
8 Quantum Monte Carlo methods
319(45)
8.1 Introduction
319(1)
8.2 Feynman path integral formulation
320(11)
8.2.1 Off-lattice problems: low temperature properties of crystals
320(7)
8.2.2 Bose statistics and superfluidity
327(1)
8.2.3 Path integral formulation for rotational degrees of freedom
328(3)
8.3 Lattice problems
331(19)
8.3.1 The Ising model in a transverse field
331(1)
8.3.2 Anisotropic Heisenberg chain
332(4)
8.3.3 Fermions on a lattice
336(2)
8.3.4 An intermezzo: the minus sign problem
338(2)
8.3.5 Spinless fermions revisited
340(2)
8.3.6 Cluster methods for quantum lattice models
342(2)
8.3.7 Continuous time simulations
344(1)
8.3.8 Decoupled cell method
345(1)
8.3.9 Handscomb's method and the stochastic series expansion (SSE) approach
346(1)
8.3.10 Wang--Landau sampling for quantum models
347(2)
8.3.11 Fermion determinants
349(1)
8.4 Monte Carlo methods for the study of groundstate properties
350(5)
8.4.1 Variational Monte Carlo (VMC)
351(2)
8.4.2 Green's function Monte Carlo methods (GFMC)
353(2)
8.5 Towards constructing the nodal surface of off-lattice, many-Fermion systems: the `survival of the fittest' algorithm
355(4)
8.6 Concluding remarks
359(5)
References
360(4)
9 Monte Carlo renormalization group methods
364(14)
9.1 Introduction to renormalization group theory
364(4)
9.2 Real space renormalization group
368(1)
9.3 Monte Carlo renormalization group
369(9)
9.3.1 Large cell renormalization
369(2)
9.3.2 Ma's method: finding critical exponents and the fixed point Hamiltonian
371(1)
9.3.3 Swendsen's method
372(2)
9.3.4 Location of phase boundaries
374(1)
9.3.5 Dynamic problems: matching time-dependent correlation functions
375(1)
9.3.6 Inverse Monte Carlo renormalization group transformations
376(1)
References
376(2)
10 Non-equilibrium and irreversible processes
378(30)
10.1 Introduction and perspective
378(1)
10.2 Driven diffusive systems (driven lattice gases)
378(3)
10.3 Crystal growth
381(3)
10.4 Domain growth
384(3)
10.5 Polymer growth
387(2)
10.5.1 Linear polymers
387(1)
10.5.2 Gelation
387(2)
10.6 Growth of structures and patterns
389(4)
10.6.1 Eden model of cluster growth
389(1)
10.6.2 Diffusion limited aggregation
389(3)
10.6.3 Cluster-cluster aggregation
392(1)
10.6.4 Cellular automata
392(1)
10.7 Models for film growth
393(5)
10.7.1 Background
393(1)
10.7.2 Ballistic deposition
394(1)
10.7.3 Sedimentation
395(1)
10.7.4 Kinetic Monte Carlo and MBE growth
396(2)
10.8 Transition path sampling
398(1)
10.9 Forced polymer pore translocation: a case study
399(3)
10.10 The Jarzynski non-equilibrium work theorem and its application to obtain free energy differences from trajectories
402(2)
10.11 Outlook: variations on a theme
404(4)
References
404(4)
11 Lattice gauge models: a brief introduction
408(15)
11.1 Introduction: gauge in variance and lattice gauge theory
408(2)
11.2 Some technical matters
410(1)
11.3 Results for Z(N) lattice gauge models
410(1)
11.4 Compact U(1) gauge theory
411(1)
11.5 SU(2) lattice gauge theory
412(1)
11.6 Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter
413(2)
11.7 The deconfinement transition of QCD
415(3)
11.8 Towards quantitative predictions
418(2)
11.9 Density of states in gauge theories
420(1)
11.10 Perspective
421(2)
References
421(2)
12 A brief review of other methods of computer simulation
423(24)
12.1 Introduction
423(1)
12.2 Molecular dynamics
423(9)
12.2.1 Integration methods (microcanonical ensemble)
423(4)
12.2.2 Other ensembles (constant temperature, constant pressure, etc.)
427(3)
12.2.3 Non-equilibrium molecular dynamics
430(1)
12.2.4 Hybrid methods (MD + MC)
430(1)
12.2.5 Ab initio molecular dynamics
431(1)
12.2.6 Hyperdynamics and metadynamics
432(1)
12.3 Quasi--classical spin dynamics
432(4)
12.4 Langevin equations and variations (cell dynamics)
436(1)
12.5 Micromagnetics
437(1)
12.6 Dissipative particle dynamics (DPD)
438(1)
12.7 Lattice gas cellular automata
439(1)
12.8 Lattice Boltzmann equation
440(1)
12.9 Multiscale simulation
440(2)
12.10 Multiparticle collision dynamics
442(5)
References
444(3)
13 Monte Carlo simulations at the periphery of physics and beyond
447(18)
13.1 Commentary
447(1)
13.2 Astrophysics
447(1)
13.3 Materials science
448(1)
13.4 Chemistry
449(2)
13.5 `Biologically inspired' physics
451(3)
13.5.1 Commentary and perspective
451(1)
13.5.2 Lattice proteins
451(2)
13.5.3 Cell sorting
453(1)
13.6 Biology
454(1)
13.7 Mathematics/statistics
455(1)
13.8 Sociophysics
456(1)
13.9 Econophysics
456(1)
13.10 `Traffic' simulations
457(2)
13.11 Medicine
459(1)
13.12 Networks: what connections really matter?
460(1)
13.13 Finance
461(4)
References
462(3)
14 Monte Carlo studies of biological molecules
465(12)
14.1 Introduction
465(1)
14.2 Protein folding
466(6)
14.2.1 Introduction
466(1)
14.2.2 How to best simulate proteins: Monte Carlo or molecular dynamics?
467(1)
14.2.3 Generalized ensemble methods
467(2)
14.2.4 Globular proteins: a case study
469(1)
14.2.5 Simulations of membrane proteins
470(2)
14.3 Monte Carlo simulations of RNA structures
472(1)
14.4 Monte Carlo simulations of carbohydrates
472(2)
14.5 Determining macromolecular structures
474(1)
14.6 Outlook
475(2)
References
475(2)
15 Outlook
477(2)
Appendix: Listing of programs mentioned in the text 479(32)
Index 511
David P. Landau is the Distinguished Research Professor of Physics and founding Director of the Center for Simulational Physics at the University of Georgia, USA. Kurt Binder is Professor Emeritus of Theoretical Physics and Gutenberg Fellow at the Institut für Physik, Johannes Gutenberg Universität, Mainz, Germany.