Monte Carlo methods in statistical physics
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| Format: | Buch |
| Sprache: | English |
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Oxford
Clarendon Press
2010
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| Ausgabe: | 1. publ., reprint. (with corr.) |
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| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036865504 | ||
| 003 | DE-604 | ||
| 005 | 20170130 | ||
| 007 | t| | ||
| 008 | 101214s2010 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9780198517979 |9 978-019-851797-9 | ||
| 035 | |a (OCoLC)706067615 | ||
| 035 | |a (DE-599)BVBBV036865504 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-11 |a DE-19 | ||
| 084 | |a UG 3100 |0 (DE-625)145625: |2 rvk | ||
| 084 | |a UG 3500 |0 (DE-625)145626: |2 rvk | ||
| 100 | 1 | |a Newman, Mark E. J. |e Verfasser |0 (DE-588)133013073 |4 aut | |
| 245 | 1 | 0 | |a Monte Carlo methods in statistical physics |c M. E. J. Newman and G. T. Barkema |
| 250 | |a 1. publ., reprint. (with corr.) | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2010 | |
| 300 | |a XIV, 475 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Literaturverz. S. [410] - 413 | ||
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistische Physik |0 (DE-588)4057000-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |D s |
| 689 | 0 | 1 | |a Statistische Physik |0 (DE-588)4057000-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Barkema, Gerard T. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020781184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020781184 | |
Datensatz im Suchindex
| DE-19_call_number | 1705/UG 3100 N554(.010) 1705/T 2 New=LS für Theoretische Physik - Quantenmaterie |
|---|---|
| DE-19_location | 95 |
| DE-BY-UBM_katkey | 5043536 |
| DE-BY-UBM_media_number | 99995484009 41623366920017 |
| DE-BY-UBR_call_number | 00/UG 3100 N554(.010) |
| DE-BY-UBR_katkey | 4725941 |
| DE-BY-UBR_location | 00 |
| DE-BY-UBR_media_number | 069040847360 |
| _version_ | 1823055543205363712 |
| adam_text | Contents
Equilibrium
Monte Carlo
simulations
Introduction
3
1.1
Statistical mechanics
.......................
З
1.2
Equilibrium
............................ 7
1.2.1
Fluctuations, correlations and responses
........ 10
1.2.2
An example: the Ising model
.............. 15
1.3
Numerical methods
........................ 18
1.3.1
Monte Carlo simulation
................. 21
1.4
A brief history of the Monte Carlo method
.......... 22
Problems
................................ 29
The principles of equilibrium thermal Monte Carlo
simulation
31
2.1
The estimator
........................... 31
2.2
Importance sampling
....................... 33
2.2.1
Markov processes
..................... 34
2.2.2
Ergodicity
......................... 35
2.2.3
Detailed balance
..................... 36
2.3
Acceptance ratios
......................... 40
2.4
Continuous time Monte Carlo
.................. 42
Problems
................................ 44
The Ising model and the Metropolis algorithm
45
3.1
The Metropolis algorithm
.................... 46
3.1.1
Implementing the Metropolis algorithm
........ 49
3.2
Equilibration
........................... 53
3.3
Measurement
........................... 57
3.3.1
Autocorrelation functions
................ 59
3.3.2
Correlation times and Markov matrices
........ 65
3.4
Calculation of errors
....................... 68
3.4.1
Estimation of statistical errors
............. 68
3.4.2
The blocking method
.................. 69
Contents
3.4.3
The bootstrap method
.................. 71
3.4.4
The jackknife method
.................. 72
3.4.5
Systematic errors
..................... 73
3.5
Measuring the entropy
...................... 73
3.6
Measuring correlation functions
................. 74
3.7
An actual calculation
....................... 76
3.7.1
The phase transition
................... 82
3.7.2
Critical fluctuations and critical slowing down
..... 84
Problems
................................ 85
Other algorithms for the Ising model
87
4.1
Critical exponents and their measurement
........... 87
4.2
The Wolff algorithm
....................... 91
4.2.1
Acceptance ratio for a cluster algorithm
........ 93
4.3
Properties of the Wolff algorithm
................ 96
4.3.1
The correlation time and the dynamic exponent
. . . 100
4.3.2
The dynamic exponent and the susceptibility
..... 102
4.4
Further algorithms for the Ising model
............. 106
4.4.1
The Swendsen-Wang algorithm
............. 106
4.4.2
Niedermayer s algorithm
................. 109
4.4.3
Multigrid methods
.................... 112
4.4.4
The invaded cluster algorithm
.............. 114
4.5
Other spin models
........................ 119
4.5.1
Potts models
....................... 120
4.5.2
Cluster algorithms for Potts models
.......... 125
4.5.3
Continuous spin models
................. 127
Problems
................................ 132
The conserved-order-parameter Ising model
133
5.1
The Kawasaki algorithm
..................... 138
5.1.1
Simulation of interfaces
................. 140
5.2
More efficient algorithms
..................... 141
5.2.1
A continuous time algorithm
.............. 143
5.3
Equilibrium crystal shapes
.................... 145
Problems
................................ 150
Disordered spin models
151
6.1
Glassy systems
.......................... 153
6.1.1
The random-field Ising model
.............. 154
6.1.2
Spin glasses
........................ 157
6.2
Simulation of glassy systems
................... 159
6.3
The
entropie
sampling method
................ 161
6.3.1
Making measurements
.................. 162
6.3.2
Internal energy and specific heat
............ 163
Contents xi
6.3.3
Implementing the
entropie
sampling method
.....164
6.3.4
An example: the random-field Ising model
.......166
6.4
Simulated tempering
.......................169
6.4.1
The method
........................169
6.4.2
Variations
.........................174
Problems
................................177
7
Ice models
179
7.1
Heal ice and ice models
..................... 179
7.1.1
Arrangement of the protons
............... 182
7.1.2
Residual entropy of ice
.................. 183
7.1.3
Three-colour models
................... 186
7.2
Monte Carlo algorithms for square ice
............. 187
7.2.1
The standard ice model algorithm
........... 188
7.2.2
Ergodicity
......................... 189
7.2.3
Detailed balance
..................... 191
7.3
An alternative algorithm
..................... 191
7.4
Algorithms for the three-colour model
............. 193
7.5
Comparison of algorithms for square ice
............ 196
7.6
Energetic ice models
....................... 201
7.6.1
Loop algorithms for energetic ice models
........ 202
7.6.2
Cluster algorithms for energetic ice models
...... 205
Problems
................................ 209
8
Analysing Monte Carlo data
210
8.1
The single histogram method
..................211
8.1.1
Implementation
......................217
8.1.2
Extrapolating in other variables
............218
8.2
The multiple histogram method
.................219
8.2.1
Implementation
......................226
8.2.2
Interpolating other variables
..............228
8.3
Finite size scaling
.........................229
8.3.1
Direct measurement of critical exponents
.......230
8.3.2
The finite size scaling method
..............232
8.3.3
Difficulties with the finite size scaling method
.....236
8.4
Monte Carlo renormalization group
...............240
8.4.1
Real-space renormalization
...............240
8.4.2
Calculating critical exponents: the exponent
ľ
.... 246
8.4.3
Calculating other exponents
...............250
8.4.4
The exponents
S
and
θ
..................251
8.4.5
More accurate transformations
.............252
8.4.6
Measuring the exponents
................256
Problems
................................258
xii Contents
II
Out-of-equilibrium
simulations
9 Out-of-equilibrium Monte Carlo
simulations
263
9.1 Dynamics............. ................264
9.1.1
Choosing the dynamics
.................266
10
Non-equilibrium simulations of the Ising model
268
10.1
Phase separation and the Ising model
............. 268
10.1.1
Phase separation in the ordinary Ising model
..... 271
10.1.2
Phase separation in the COP Ising model
....... 271
10.2
Measuring domain size
...................... 274
10.2.1
Correlation functions
................... 274
10.2.2
Structure factors
..................... 277
10.3
Phase separation in the
3D
Ising model
............ 278
10.3.1
A more efficient algorithm
................ 279
10.3.2
A continuous time algorithm
.............. 280
10.4
An alternative dynamics
..................... 282
10.4.1
Bulk diffusion and surface diffusion
........... 283
10.4.2
A bulk diffusion algorithm
................ 284
Problems
................................ 288
11
Monte Carlo simulations in surface science
289
11.1
Dynamics, algorithms and energy barriers
........... 292
11.1.1
Dynamics of a single
adatom
.............. 293
11.1.2
Dynamics of many adatoms
............... 296
11.2
Implementation
.......................... 301
11.2.1
Kawasaki and bond-counting algorithms
........ 301
11.2.2
Lookup table algorithms
................. 302
11.3
An example: molecular beam epitaxy
.............. 304
Problems
................................ 306
12
The repton model
307
12.1
Electrophoresis
..........................307
12.2
The repton model
.........................309
12.2.1
The projected repton model
...............313
12.2.2
Values of the parameters in the model
.........314
12.3
Monte Carlo simulation of the repton model
..........315
12.3.1
Improving the algorithm
.................316
12.3.2
Further improvements
..................318
12.3.3
Representing configurations of the repton model
. . . 320
12.4
Results of Monte Carlo simulations
...............322
12.4.1
Simulations in zero electric field
.............323
12.4.2
Simulations in non-zero electric field
..........323
Problems
................................327
Contents
лі
III
Implementation
13
Lattices and data structures
331
13.1
Representing lattices on a computer
..............332
13.1.1
Square and cubic lattices
................ 332
13.1.2
Triangular, honeycomb and
Kagomé
lattices
...... 335
13.1.3
Fee, bec and diamond lattices
.............. 340
13.1.4
General lattices
...................... 342
13.2
Data structures
.......................... 343
13.2.1
Variables
......................... 343
13.2.2
Arrays
........................... 345
13.2.3
Linked lists
........................ 345
13.2.4
Trees
............................ 348
13.2.5
Buffers
........................... 352
Problems
................................ 355
14
Monte Carlo simulations on parallel computers
356
14.1
Trivially parallel algorithms
...................358
14.2
More sophisticated parallel algorithms
.............359
14.2.1
The
bing
model with the Metropolis algorithm
.... 359
14.2.2
The Ising model with a cluster algorithm
.......361
Problems
................................362
15
M
ultispin
coding
364
15.1
The
bing
model
.........................365
15.1.1
The one-dimensional Ising model
............ 365
15.1.2
The two-dimensional Ising model
............ 367
15.2
Implementing multispin-coded algorithms
........... 369
15.3
Truth tables and Karnaugh maps
................ 369
15.4
A multispin-coded algorithm for the repton model
...... 373
15.5
Synchronous update algorithms
................. 379
Problems
................................ 380
16
Random numbers
382
16.1
Generating uniformly distributed random numbers
......382
16.1.1
True random numbers
.................. 384
16.1.2
Pseudo-random numbers
................. 385
16.1.3
Linear congruential generators
............. 386
16.1.4
Improving the linear congruential generator
...... 390
16.1.5
Shift register generators
................. 392
16.1.6
Lagged Fibonacci generators
.............. 393
16.2
Generating non-uniform random numbers
........... 396
16.2.1
The transformation method
...............396
16.2.2
Generating Gaussian random numbers
.........399
Contents
16.2.3
The rejection method
.................. 401
16.2.4
The hybrid method
.................... 404
16.3
Generating random bits
..................... 406
Problems
................................ 409
References
410
Appendices
A Answers to problems
417
В
Sample programs
433
B.I Algorithms for the Ising model
.................433
B.I.I Metropolis algorithm
...................433
B.1.2 Multispin-coded Metropolis algorithm
.........435
B.1.3 Wolff algorithm
. . . .,..................437
B.2 Algorithms for the COP Ising model
..............438
B.2.1 Non-local algorithm
...................438
B.2.2 Continuous time algorithm
...............441
B.3 Algorithms for Potts models
...................445
B.4 Algorithms for ice models
....................448
B.5 Random number generators
...................451
B.5.1 Linear congruential generator
..............451
B.5.2 Shuffled linear congruential generator
.........452
B.5.3 Lagged Fibonacci generator
...............452
Index
455
|
| any_adam_object | 1 |
| author | Newman, Mark E. J. Barkema, Gerard T. |
| author_GND | (DE-588)133013073 |
| author_facet | Newman, Mark E. J. Barkema, Gerard T. |
| author_role | aut aut |
| author_sort | Newman, Mark E. J. |
| author_variant | m e j n mej mejn g t b gt gtb |
| building | Verbundindex |
| bvnumber | BV036865504 |
| classification_rvk | UG 3100 UG 3500 |
| ctrlnum | (OCoLC)706067615 (DE-599)BVBBV036865504 |
| discipline | Physik |
| edition | 1. publ., reprint. (with corr.) |
| format | Book |
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| id | DE-604.BV036865504 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:41:49Z |
| institution | BVB |
| isbn | 9780198517979 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020781184 |
| oclc_num | 706067615 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM |
| physical | XIV, 475 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Clarendon Press |
| record_format | marc |
| spellingShingle | Newman, Mark E. J. Barkema, Gerard T. Monte Carlo methods in statistical physics Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4057000-9 |
| title | Monte Carlo methods in statistical physics |
| title_auth | Monte Carlo methods in statistical physics |
| title_exact_search | Monte Carlo methods in statistical physics |
| title_full | Monte Carlo methods in statistical physics M. E. J. Newman and G. T. Barkema |
| title_fullStr | Monte Carlo methods in statistical physics M. E. J. Newman and G. T. Barkema |
| title_full_unstemmed | Monte Carlo methods in statistical physics M. E. J. Newman and G. T. Barkema |
| title_short | Monte Carlo methods in statistical physics |
| title_sort | monte carlo methods in statistical physics |
| topic | Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Monte-Carlo-Simulation Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020781184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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