Introduction to phase transitions and critical phenomena:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Oxford Univ. Pr.
1987
|
| Edition: | 1. iss. as an Oxford Univ. Pr. paperback, 3. pr. |
| Series: | The international series of monographs on physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 290 - 300 |
| Physical Description: | XX, 308 S. Ill., graph. Darst. |
| ISBN: | 0195053168 |
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| 245 | 1 | 0 | |a Introduction to phase transitions and critical phenomena |c by H. Eugene Stanley |
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| 264 | 1 | |a New York u.a. |b Oxford Univ. Pr. |c 1987 | |
| 300 | |a XX, 308 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804117834709598208 |
|---|---|
| adam_text | CONTENTS
NOTATION GUIDE
xv
PAST I
INTRODUCTION
1.
WHAT ARE THE CRITICAL
ΡΗΕΝΟΜΕΝΑΓ
A SURVEY
OF SOME BASIC RESULTS I
1.1.
Classical era of critical phenomena
1
1.2.
Modern era of critical phenomena
9
1.3.
Phase transitions in other systems
18
2.
USEFUL THERMODYNAMIC RELATIONS FOR FLUID
AND MAGNETIC SYSTEMS
22
2.1.
The thermodynamic state functions
17,
E, G, and A
22
2.2.
Differential relations for the state functions: the thermodynamic
square
23
2.3.
Two basic response functions: the specific heat and the com¬
pressibility
25
2.4.
Stability and convexity relations
28
2.5.
Geometrical interpretation of the Gibbs and Hclmholtz
potentials
30
2.6.
Analogies between fluids and magnets
32
2.7.
The thermodynamic state functions for a magnetic system
33
2.8.
Differential relations and the thermodynamic square for mag¬
netic state functions
33
2.9.
Magnetic response functions: specific heat and susceptibility
35
2.10.
Convexity relations for magnetic systems
36
2.11.
Geometrical interpretations of the thermodynamic potentials for
a magnetic system
37
FABI II
CRITICAL-POINT EXPONENTS AND RIGOROUS
RELATIONS AMONG THEM
3.
CRITICAL-POINT EXPONENTS
39
3.1.
Definition of a critical-point exponent
39
3.2.
The critical-point exponents
α, β, γ,
б,
v,
and
η
42
3.3.
Numerical values of critical-point exponents
46
3.4.
The exponents
Δ
and
9 49
3.5.
Useful relations among critical-point exponents
51
xii CONTENTS
4. EXPONENT
INEQUALITIES
4.1.
The Rushbrooke and Coopersmith inequalities
63
4.2.
The Griffiths inequality
66
4.3.
More inequalities
60
PABX
III
CLASSICAL THEORIES OF COOPERATIVE PHENOMENA
fî.
THE VAN
DER WAALS
THEORY OF LIQUID-GAS
PHASE TRANSITIONS
67
6.1.
Heuristic derivation of the van
der Waals
equation of state
67
5.2.
van
der Waals
isotherms and the Maxwell construction
69
5.3.
The van
der Waals
critical point
71
5.4.
The law of corresponding states
72
5.6.
Critical-point exponents for the van
der Waals
theory
74
5.6.
The van
der Waals
equation of state as a mean field theory
76
6.
THE MEAN FIELD THEORY OF MAGNETIC PHASE
TRANSITIONS
79
6.1.
The non-interacting magnetic system
80
6.2.
The assumption of an effective molecular field
82
6.3.
Critical-point exponents for the mean field theory
84
6.4.
The mean field theory as an approximation for the
Heisenberg
model
89
6.5.
Equivalence of the mean field theory and an infinite interaction
range
91
7.
THE PAIR CORRELATION FUNCTION AND THE
ORNSTEIN-ZERNIKE THEORY
94
7.1.
The density-density correlation function for a fluid system
94
7.2.
Relation between density fluctuations, the isothermal com¬
pressibility, and the density-density correlation function
96
7.3.
The structure factor: relation between the pair correlation
function and the scattering of electromagnetic radiation
98
7.4.
Ornstein-Zernike theory of the scattering amplitude
100
7.6.
Further developments of the Ornstein-Zemike theory
106
PAKT
IV
MODELS OF FLUID AND MAGNETIC PHASE
TRANSITIONS
8.
RESULTS PROVIDED BY EXACT SOLUTION OF
MODEL SYSTEMS
109
8.1.
A model Hamiltonian for a classical spin system: the generalized
Heisenberg
model
110
8.2.
Exact solution of the case
d
= 1,
D
= 1,
H
= 0:
The linear
chain Ising model in the absence of an external magnetic field
115
8.3.
The linear chain of arbitrary dimensional spins in zero magnetic
field
124
8.4.
The spherical model as the limit of infinite spin dimensionality
128
CONTENTS xiii
8.5.
The transfer matrix method: application to the
d
= 1
Ising
model in a magnetic field
131
9.
RESULTS OBTAINED FROM MODEL SYSTEMS BY
APPROXIMATION METHODS
134
9.1.
Successive approximation concept
135
9.2.
Series expansion methods
136
9.3.
Calculation of the coefficients in the high-temperature expansion
of the partition function
138
9.4.
Calculation of the coefficients in the high-temperature expansion
of the two-spin correlation function
146
9.5.
Physical interpretation of the terms in the high-temperature
expansion of the correlation function
148
9.6.
Extrapolation procedures for estimating the limiting behaviour
of a power series from the behaviour of its first few terms
152
9.7.
Padé approximants
and transformation methods
158
9.8.
Conclusions
164
PAKT
V
PHENOMENOLOGICAL THEORIES OF PHASE
TRANSITIONS
10.
LANDAU S CLASSIC THEORY OF EXPONENTS
167
10.1.
Expansions about the critical point
167
10.2.
Assumptions of the Landau theory
168
10.3.
Critical-point predictions of the Landau theory
170
10.4.
Critique of the
Landau
theory
172
11.
SCALING LAW HYPOTHESIS FOR THERMODYNAMIC
FUNCTIONS
175
11.1.
Homogeneous functions of one or more variables
176
11.2.
Static scaling hypothesis
181
11.3.
Predicted relations among the critical-point exponents
182
11.4.
Magnetic equation of state: scaled magnetization and scaled
magnetic field
185
12.
SCALING OF THE STATIC CORRELATION FUNCTIONS
191
12.1.
The Kadanoff construction
191
12.2.
Application to the pair correlation function
194
12.3.
Alternative methods of obtaining the correlation function
scaling relations
197
12.4.
Comparison with model calculations
199
FABT VI
DYNAMIC ASPECTS OF CRITICAL PHENOMENA
13.
INTRODUCTION TO DYNAMIC CRITICAL
PHENOMENA IN FLUID SYSTEMS
202
13.1.
Critical-point exponents for transport coefficients
203
13.2.
Time-dependent correlation functions and the dynamic structure
factor
Sř
(q,
ω)
204
xiv CONTENTS
13.3. Relation
between the dynamic structure factor and light-
scattering experiments
205
13.4.
Predictions of hydrodynamics for the spectrum of the scattered
radiation
210
13.5.
Predictions of hydrodynamics near the critical point
214
14.
MEASUREMENTS OF THE DYNAMIC STRUCTURE
FACTOR FOR FLUID SYSTEMS
217
14.1.
Time-dependent density fluctuations
217
14.2.
Optical mixing spectroscopy
218
14.3.
Measurements of the Rayleigh linewidth
219
14.4.
Corrections to the hydrodynamic theory of the Rayleigh linewidth
225
14.5.
Measurements of the Brillouin peak: velocity and attenuation of
hypersonic sound waves
228
15.
DYNAMIC SCALING LAWS AND THE MODE-MODE
COUPLING APPROXIMATION
233
15.1.
Dynamic scaling hypothesis
233
15.2.
Predictions of the restricted dynamic scaling hypothesis for
fluid systems
236
15.3.
Predictions of extended dynamic scaling for fluid systems
238
15.4.
Evidence supporting the dynamic scaling hypothesis provided by
magnetic systems
240
15.5.
Spirit of the mode-mode coupling approach
246
16.6.
Predictions of the mode-mode coupling approximation
249
15.7.
Application of the mode-mode coupling approach to the inter¬
pretation of experimental results on fluids
254
15.8.
Applications of the mode-mode coupling approach to other
systems
259
APPENDIX A. The lattice-gas model of a fluid system
260
APPENDIX B. Exact solution of the zero-field Ising model for a two-
dimensional lattice
265
APPENDIX C. Geometric interpretation of the static scaling hypothe¬
sis for thermodynamic potentials
272
APPENDIX D. The dynamic structure factor in the hydrodynamie
limit
275
APPENDIX E. Model systems useful in the study of time-dependent
cooperative phenomena: the Glauber model
280
APPENDIX F. Two-dimensional ferroelectric and antiferroelectric
modete
287
BIBLIOGRAPHY
290
AUTHOR INDEX
301
SUBJECT INDEX
305
|
| any_adam_object | 1 |
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| author_facet | Stanley, H. Eugene 1941- |
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| dewey-ones | 530 - Physics |
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| discipline | Physik |
| edition | 1. iss. as an Oxford Univ. Pr. paperback, 3. pr. |
| format | Book |
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| indexdate | 2024-07-09T16:00:42Z |
| institution | BVB |
| isbn | 0195053168 |
| language | English |
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| physical | XX, 308 S. Ill., graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
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| publisher | Oxford Univ. Pr. |
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| series2 | The international series of monographs on physics |
| spelling | Stanley, H. Eugene 1941- Verfasser (DE-588)124434851 aut Introduction to phase transitions and critical phenomena by H. Eugene Stanley 1. iss. as an Oxford Univ. Pr. paperback, 3. pr. New York u.a. Oxford Univ. Pr. 1987 XX, 308 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on physics Literaturverz. S. 290 - 300 Festkörper (DE-588)4016918-2 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Kritisches Phänomen (DE-588)4165788-3 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s DE-604 Festkörper (DE-588)4016918-2 s Kritisches Phänomen (DE-588)4165788-3 s 1\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002210702&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stanley, H. Eugene 1941- Introduction to phase transitions and critical phenomena Festkörper (DE-588)4016918-2 gnd Phasenumwandlung (DE-588)4132140-6 gnd Kritisches Phänomen (DE-588)4165788-3 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4132140-6 (DE-588)4165788-3 |
| title | Introduction to phase transitions and critical phenomena |
| title_auth | Introduction to phase transitions and critical phenomena |
| title_exact_search | Introduction to phase transitions and critical phenomena |
| title_full | Introduction to phase transitions and critical phenomena by H. Eugene Stanley |
| title_fullStr | Introduction to phase transitions and critical phenomena by H. Eugene Stanley |
| title_full_unstemmed | Introduction to phase transitions and critical phenomena by H. Eugene Stanley |
| title_short | Introduction to phase transitions and critical phenomena |
| title_sort | introduction to phase transitions and critical phenomena |
| topic | Festkörper (DE-588)4016918-2 gnd Phasenumwandlung (DE-588)4132140-6 gnd Kritisches Phänomen (DE-588)4165788-3 gnd |
| topic_facet | Festkörper Phasenumwandlung Kritisches Phänomen |
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