Advanced statistical mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | International series of monographs on physics
146 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Literaturangaben |
| Beschreibung: | XV, 624 S. graph. Darst. |
| ISBN: | 9780199556632 9780198744269 0199556636 |
Internformat
MARC
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| 100 | 1 | |a McCoy, Barry M. |e Verfasser |0 (DE-588)114146047 |4 aut | |
| 245 | 1 | 0 | |a Advanced statistical mechanics |c Barry M. McCoy |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XV, 624 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs on physics |v 146 | |
| 490 | 0 | |a Oxford science publications | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Statistical mechanics | |
| 650 | 4 | |a Statistical mechanics | |
| 650 | 0 | 7 | |a Statistische Mechanik |0 (DE-588)4056999-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Statistische Mechanik |0 (DE-588)4056999-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a International series of monographs on physics |v 146 |w (DE-604)BV000106406 |9 146 | |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018804341 | ||
Datensatz im Suchindex
| _version_ | 1804140937746579456 |
|---|---|
| adam_text | Contents
PART I GENERAL THEORY
Basic principles
3
1.1
Thermodynamics
3
1.1.1
Macroscopic, extensive and intensive
3
1.1.2
Equilibrium
5
1.1.3
The four laws of thermodynamics
6
1.2
Statistical mechanics
9
1.2.1
Statistical philosophy
9
1.2.2
The microcanonical ensemble
10
1.2.3
The canonical ensemble
11
1.2.4
The grand canonical ensemble
15
1.2.5
Phases and ergodic components
17
1.3
Quantum statistical mechanics
17
1.3.1
The relation of classical to quantum statistical mechanics
18
1.4
Quantum field theory
19
References
21
Reductionism, phenomena and models
22
2.1
Reductionism
22
2.2
Phenomena
24
2.2.1
Monatomic insulators
24
2.2.2
Diatomic insulators
25
2.2.3
Liquid crystals
28
2.2.4
Water
28
2.2.5
Metals
29
2.2.6
Helium
29
2.2.7
Magnetic transitions
30
2.3
Models
33
2.3.1
Continuum models
34
2.3.2
Lattice models
37
2.4
Discussion
41
2.5
Appendix:
Bravais
lattices
42
References
44
Stability, existence and uniqueness
45
3.1
Classical stability
49
3.1.1
Catastrophic potentials
49
3.1.2
Conditions for stability
49
3.1.3
Superstability
57
χ
Contents
3.1.4 Multispecies
interactions
59
3.2 Quantum
stability
61
3.2.1
Stability of
matter 61
3.2.2
Proofs of theorems
1
and
2 63
3.3
Existence and uniqueness of the thermodynamic limit
66
3.3.1
Box boundary conditions
67
3.3.2
Periodic boundary conditions
69
3.3.3
Existence and uniqueness in the canonical ensemble
69
3.3.4
Existence and uniqueness in the grand canonical ensemble
77
3.3.5
Continuity of the pressure
78
3.4
First order phase transitions, zeros and analyticity
80
3.5
Discussion
82
3.6
Open questions
84
3.7
Appendix A: Properties of functions of positive type
85
3.8
Appendix B: Fourier transforms
86
References
90
4
Theorems on order
92
4.1
Densest packing of hard spheres and ellipsoids
93
4.2
Lack of order in the
isotropie
Heisenberg
model in
D
= 1, 2 97
4.3
Lack of crystalline order in
D
= 1, 2 103
4.4
Existence of ferromagnetic and antiferromagnetic order in the
classical
Heisenberg
model (n vector model) in
D
= 3 110
4.4.1
The mechanism for ferromagnetic order 111
4.4.2
Proof of the bound
(4.123) 113
4.4.3
Antiferromagnetism
117
4.5
Existence of antiferromagnetic order in the quantum
Heisenberg
model for
Τ
> 0
and
D
= 3 118
4.6
Existence of antiferromagnetic order in the quantum
Heisenberg
model for
Τ
= 0
and
D
= 2 120
4.7
Missing theorems
120
References
122
5
Critical phenomena and scaling theory
124
5.1
Thermodynamic critical exponents and inequalities for Ising-like
systems
125
5.2
Scalingjiheory for Ising-like systems
128
5.2.1
Scaling for
Я
= 0 129
5.2.2
Scaling for
Η φ
0 132
5.2.3
Summary of critical exponent equalities
136
5.3
Scaling for general systems
136
5.3.1
The classical
η
vector and quantum
Heisenberg
models
137
5.3.2
Lennard-Jones fluids
142
5.4
Universality
142
5.5
Missing theorems
143
References
145
Contents xi
PART II SERIES
AND NUMERICAL METHODS
Mayer virial expansions and Groeneveld s theorems
149
6.1
The second virial coefficient
156
6.2
Mayers first theorem 15g
6.3
Mayers second theorem
160
6.3.1
Step
1 160
6.3.2
Step
2 162
6.3.3
Step
3 164
6.4
Non-negative potentials and Groeneveld s theorems
167
6.5
Convergence of virial expansions
173
6.6
Counting of Mayer graphs
176
6.7
Appendix: The irreducible Mayer graphs of four and five points
178
References
180
Ree—
Hoover virial expansion and hard particles
181
7.1
The Ree-Hoover expansion
182
7.2
The Tonks Gas
186
7.3
Hard sphere virial coefficients B2-B4 in two and higher dimen¬
sions
189
7.3.1
Evaluation of B2
189
7.3.2
Evaluation of B3
191
7.3.3
Evaluation of B4
194
7.4
Monte-Carlo evaluations of
B¿-B q
195
7.5
Hard sphere virial coefficients for
к
> 11 196
7.6
Radius of convergence and approximate equations of state
198
7.7
Parallel hard squares, parallel hard cubes and hard hexagons on
a lattice
202
7.8
Convex nonspherical hard particles
204
7.9
Open questions
205
References
208
High density expansions
210
8.1
Molecular dynamics
211
8.2
Hard spheres and discs
212
8.2.1
Behavior near close packing
213
8.2.2
Freezing of hard spheres
214
8.2.3
The phase transition for hard discs
219
8.3
The inverse power law potential
222
8.3.1
Scaling behavior
223
8.3.2
Numerical computations
224
8.4
Hard spheres with an additional square well
225
8.5
Lennard-Jones potentials
227
8.6
Conclusions
228
References
230
xü Contents
9
High temperature expansions for magnets at
H
= 0 232
9.1
Classical
η
vector model for
D
= 2, 3 234
9.1.1
Results for
D
= 2 237
9.1.2
A qualitative interpretation of the
D
= 2
data
240
9.1.3
Results for
D
= 3 242
9.1.4
Critical exponents
243
9.1.5
The ratio method
248
9.1.6
Estimates from differential approximates
254
9.2
Quantum
Heisenberg
model
255
9.2.1
Results for
D
= 2 257
9.2.2
Results for
D
= 3 258
9.2.3
Analysis of results
259
9.3
Discussion
261
9.4
Statistical mechanics versus quantum field theory
265
9.5
Appendix: The expansion coefficients for the susceptibility on the
square lattice
267
References
272
PART III EXACTLY SOLVABLE MODELS
10
The Ising model in two dimensions: summary of results
277
10.1
The homogeneous lattice at
Я
= 0 280
10.1.1
Partition function on the torus
280
10.1.2
Zeros of the partition function
281
10.1.3
Bulk free energy per site
283
10.1.4
Partition function at
Τ
=
Tc
286
10.1.5
Spontaneous magnetization
286
10.1.6
Row and diagonal spin correlation functions
287
10.1.7
The correlation C(M, N) for general
Μ, Ν
295
10.1.8
Scaling limit
297
10.1.9
Magnetic susceptibility of the bulk
302
10.1.10
The diagonal susceptibility
306
10.2
Boundary properties of the homogeneous lattice at
Η
= 0 309
10.2.1
Boundary free energy at Hb
= 0 309
10.2.2
Boundary magnetization Mi(Hb)
310
10.2.3
Boundary spin correlations
312
10.2.4
Analytic continuation and hysteresis
314
10.3
The layered random lattice
316
10.4
The Ising model for
Я
φ
0 319
10.4.1
The circle theorem
319
10.4.2
The imaginary magnetic field H/kBT
=
¿π/2
319
10.4.3
Expansions for small
Я
321
10.4.4
Τ
= TC with
Я
> 0 322
10.4.5
Extended analyticity
323
References
324
Contents xiii
11
The Pfaffian solution of the Ising model
328
11.1
Dimers
329
11.1.1
Dimers on lattices with free boundary conditions
330
11.1.2
Dimers on a cylinder
337
11.1.3
Dimers on lattices of genus
g
> 1 338
11.1.4
Explicit evaluation of the Pfaffians
339
11.1.5
Thermodynamic limit
344
11.1.6
Other lattices and boundary conditions
345
11.2
The Ising partition function
347
11.2.1
Toroidal (periodic) boundary conditions
347
11.2.2
Cylindrical boundary conditions
354
11.3
Correlation functions
355
11.3.1
The correlation
(cta/.tv^m.tv)
355
11.3.2
The diagonal correlation
(cto^ctív.w)
359
11.3.3
Correlations near the boundary
360
References
361
12
Ising model spontaneous magnetization and form factors
363
12.1 Wiener-Hopf
sum equations
364
12.1.1
Fourier transforms
364
12.1.2
Splitting and factorization
366
12.1.3
Solution
367
12.2
Spontaneous magnetization and
Szegö s
theorem
368
12.2.1
Proof of
Szegö s
theorem
369
12.2.2
The spontaneous magnetization
374
12.3
Form factor expansions of C{N, TV) and C(0.
Лг)
375
12.3.1
Expansion for
Τ
<
Tc
375
12.3.2
Expansion for
Τ
>
Tc
386
12.4
Asymptotic expansions of
С
(TV. TV) and C(0. TV) for TV
-+
oc
392
12.4.1
Large TV for
Τ
<
Tc
392
12.4.2
Large TV for
Τ
>
Tc
393
12.4.3
Large TV for
Τ
=
Tc
393
12.5
Evaluation of diagonal form factor integrals
398
12.5.1
Differential equations
399
12.5.2
Factorization and direct sums
399
12.5.3
Homomorphisms of operators
402
12.5.4
Symmetric powers
402
12.5.5
Results
404
12.5.6
Discussion
406
References
407
13
The star-triangle (Yang-Baxter) equation
408
13.1
Historical overview
408
13.2
Transfer matrices
412
13.2.1
Explicit forms of the transfer matrix
415
13.2.2
The physical regime
416
xiv Contents
13.3 Integrability 417
13.4
Star-triangle equation for vertex models
418
13.4.1
Boltzmann weights for two-state vertex models
419
13.4.2
Vertex-spin correspondence
436
13.4.3
Inhomogeneous lattices
439
13.5
Star-triangle equation for spin models
440
13.5.1
Chiral Potts model
440
13.5.2
Proof of the star-triangle equation
448
13.5.3
Determination of Rpqr
451
13.6
Star-triangle equation for face models
452
13.6.1
SOS and RSOS models
452
13.6.2
The hard hexagon model
457
13.7
Hamiltonian limits
464
13.7.1
Spin chains for the eight- and six-vertex models
466
13.7.2
Spin chain for the chiral Potts model
469
13.8
Appendix: Properties of theta functions
472
References
477
14
The eight-vertex and XYZ model
480
14.1
Historical overview
481
14.2
The matrix TQ equation for the eight-vertex model
484
14.2.1
Modified theta functions
486
14.2.2
Formal construction of the matrices Qi2{v)
488
14.2.3
Explicit construction of Qr{v) and Ql{v)
489
14.2.4
The interchange relation
498
14.2.5
Nonsingularity and nondegeneracy
508
14.2.6
Quasiperiodicity
509
14.3
Eigenvalues and free energy
514
14.3.1
The form of the eigenvalues
514
14.3.2
Numerical study of the eigenvalues of Qj2{v)
516
14.3.3
Bethe s equation
526
14.3.4
Computation of the free energy
528
14.4
Excitations, order parameters and correlation functions of the
eight- and six-vertex model
537
14.4.1
Eight-vertex polarization P8 and XYZ order
538
14.4.2
Eight-vertex magnetization M8
541
14.4.3
Correlations for the XY model
542
14.4.4
XYZ correlations
550
14.5
Appendix: Properties of the modified theta functions
552
References
557
15
The hard hexagon, RSOS and chiral Potts models
562
15.1
The hard hexagon and RSOS models
562
15.1.1
Historical overview
552
15.1.2
Hard hexagons for
0 <
ζ
<
zc
565
15.1.3
Hard hexagons for zc
<
ζ
<
oc
571
Contents xv
15.1.4
Discussion
574
15.2
The chiral Potts model
575
15.2.1
Historical overview
575
15.2.2
Real and positive Boltzmann weights
578
15.2.3
The superintegrable chiral Potts model and Onsager s al¬
gebra
585
15.2.4
The functional equation for the superintegrable case for
N = 3 588
15.2.5
Superintegrable ground state energy for small
λ
590
15.2.6
Single particle excitations and level crossing
595
15.2.7
Order parameter
598
15.2.8
The phase diagram of the spin chain
599
15.3
Open questions
600
15.3.1
Q
operators
601
15.3.2
Degenerate subspaces for the eight-vertex model
602
15.3.3
Symmetry algebra for the eight-vertex model at roots of
unity
603
15.3.4
Chiral Potts correlations
603
References
605
PART IV CONCLUSION
16
Reductionism versus complexity
613
16.1
Does history matter?
613
16.2
Size is important
615
16.3
The paradox of integrability
616
16.4
Conclusion
617
References
618
Index
619
|
| any_adam_object | 1 |
| author | McCoy, Barry M. |
| author_GND | (DE-588)114146047 |
| author_facet | McCoy, Barry M. |
| author_role | aut |
| author_sort | McCoy, Barry M. |
| author_variant | b m m bm bmm |
| building | Verbundindex |
| bvnumber | BV035947224 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.8 |
| callnumber-search | QC174.8 |
| callnumber-sort | QC 3174.8 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 3100 |
| classification_tum | PHY 057f |
| ctrlnum | (OCoLC)435730815 (DE-599)BVBBV035947224 |
| dewey-full | 530.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.13 |
| dewey-search | 530.13 |
| dewey-sort | 3530.13 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035947224 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:07:55Z |
| institution | BVB |
| isbn | 9780199556632 9780198744269 0199556636 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018804341 |
| oclc_num | 435730815 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-83 |
| owner_facet | DE-20 DE-703 DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-83 |
| physical | XV, 624 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics Oxford science publications |
| spelling | McCoy, Barry M. Verfasser (DE-588)114146047 aut Advanced statistical mechanics Barry M. McCoy 1. publ. Oxford [u.a.] Oxford Univ. Press 2010 XV, 624 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 146 Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Literaturangaben Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s DE-604 International series of monographs on physics 146 (DE-604)BV000106406 146 V:DE-604 application/pdf http://media.obvsg.at/AC08027992-1001 BVB-CE Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McCoy, Barry M. Advanced statistical mechanics International series of monographs on physics Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 |
| title | Advanced statistical mechanics |
| title_auth | Advanced statistical mechanics |
| title_exact_search | Advanced statistical mechanics |
| title_full | Advanced statistical mechanics Barry M. McCoy |
| title_fullStr | Advanced statistical mechanics Barry M. McCoy |
| title_full_unstemmed | Advanced statistical mechanics Barry M. McCoy |
| title_short | Advanced statistical mechanics |
| title_sort | advanced statistical mechanics |
| topic | Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistical mechanics Statistische Mechanik |
| url | http://media.obvsg.at/AC08027992-1001 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT mccoybarrym advancedstatisticalmechanics |
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Inhaltsverzeichnis