Physics of critical fluctuations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1995
|
| Series: | Graduate texts in contemporary physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 375 - 386 |
| Physical Description: | XV, 390 S. graph. Darst. |
| ISBN: | 0387944141 |
Staff View
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| 100 | 1 | |a Ivančenko, Julij M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Physics of critical fluctuations |c Yuli M. Ivanchenko ; Alexander A. Lisyansky |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
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Record in the Search Index
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| adam_text | YULI M. IVANCHENKO ALEXANDER A. LISYANSKY PHYSICS OF CRITICAL
FLUCTUATIONS WITH 121 ILLUSTRATIONS SPRINGER CONTENTS PREFACE V 1
CLASSICAL APPROACH 1 1.1 INTRODUCTION 1 1.2 LANDAU THEORY 2 1.2.1 THE
SCALAR ORDER PARAMETER 3 1.2.2 THE VECTOR ORDER PARAMETER 4 1.3 BROKEN
SYMMETRY AND CONDENSATION 5 1.3.1 BOSE-EINSTEIN CONDENSATION 9 1.4
ERGODICITY 11 1.4.1 SUSCEPTIBILITY 12 1.4.2 THE ERGODIC HYPOTHESIS 12
1.5 GAUSSIAN APPROXIMATION 14 1.5.1 GOLDSTONE BRANCH OF EXCITATIONS 15
1.5.2 CORRELATION FUNCTIONS 16 1.5.3 MICROSCOPIC SCALES IN PHASE
TRANSITIONS 17 1.6 THE GINZBURG CRITERION 18 1.6.1 CRITICAL DIMENSIONS
20 1.7 THE SCALING HYPOTHESIS 24 1.7.1 SCALING LAWS 25 2 THE
GINZBURG-LANDAU FUNCTIONAL 29 2.1 INTRODUCTION 29 2.2 CLASSICAL SYSTEMS
30 2.2.1 THE ISING MODEL 30 2.2.2 THE HEISENBERG MODEL 35 2.2.3
INTERACTING PARTICLES 40 2.3 QUANTUM SYSTEMS 51 2.3.1 THE HEISENBERG
HAMILTONIAN 52 2.3.2 BOSE GAS 53 XI XII CONTENTS 2.3.3 BOSE-EINSTEIN
CONDENSATION 57 2.3.4 FERMI GAS 59 3 WILSON S RENORMALIZATION SCHEME 65
3.1 INTRODUCTION 65 3.2 KADANOFF S INVARIANCE 67 3.3 WILSON S THEORY 69
3.3.1 DERIVATION OF THE RG EQUATION 70 3.3.2 LINEARIZED RG EQUATION 78
3.3.3 REDUNDANT EIGENVECTORS 83 3.3.4 SCALING PROPERTIES AND CRITICAL
EXPONENTS 89 3.3.5 GAUSSIAN FIXED POINT 95 3.3.6 THE SCALING-FIELD
METHOD 99 3.3.7 6-EXPANSION IN SCALING FIELDS 103 4 FIELD THEORETICAL RG
109 4.1 INTRODUCTION 109 4.2 PERTURBATION THEORY 110 4.2.1 GENERAL
DEFINITIONS 110 4.2.2 GRAPH EQUATIONS FOR 0 4 -MODEL 115 4.2.3 RULES OF
EVALUATION 117 4.2.4 REGULARIZATION 118 4.3 RENORMALIZATION 119 4.3.1
CALCULUS OF DIVERGENCES 120 4.3.2 SIMPLE GENERALIZATIONS 122 4.3.3
MULTIPLICATIVE GROUP EQUATIONS 124 4.3.4 SCALING PROPERTIES 127 4.3.5
DIFFERENTIAL GROUP EQUATIONS 128 4.4 SCALING LAWS 129 4.5 *-EXPANSION
133 4.5.1 ADDITION OF COUNTER-TERMS 134 4.5.2 AN ALTERNATIVE APPROACH
135 4.5.3 RESULTS 136 4.5.4 CORRECTION TO SCALING 138 4.5.5 IMPROVEMENT
OF CONVERGENCE 138 4.6 EXPANSIONS AT D * 3 139 4.6.1 COMPARISON OF
MASSIVE AND MASSLESS THEORIES . . . . 141 4.6.2 EXPERIMENTAL SITUATION
142 4.7 RESULTS OF DIFFERENT APPROACHES 144 CONTENTS XIII 5 GENERALIZED
RG APPROACH 147 5.1 INTRODUCTION 147 5.2 SCALE TRANSFORMATIONS 148 5.2.1
DIFFERENTIAL FORM OF SCALE COVARIANCE 149 5.2.2 TWO WAYS OF UTILIZING
SCALE COVARIANCE 150 5.3 SCALE EQUATIONS 151 5.3.1 CONVENTIONAL APPROACH
151 5.3.2 GENERALIZED APPROACH 154 5.4 RG EQUATIONS 155 5.4.1
CONVENTIONAL APPROACH 156 5.4.2 GENERALIZED APPROACH 157 5.4.3 RG AS A
CHARACTERISTIC SET OF SCALE EQUATIONS . . . . 159 5.5 APPLICATIONS OF
GENERALIZED SE 160 5.5.1 STRUCTURE OF THE CORRELATION FUNCTION AT THE
TRANSI TION POINT 161 5.5.2 FUNCTION R}(Q) AT THE FIXED POINT 163 5.6
^EXPANSION 166 5.6.1 GENERAL SCHEME OF THE METHOD 167 5.6.2 SOLUTION OF
EQUATIONS 171 5.6.3 EVALUATION OF THE ^EXPONENT 172 5.6.4 EVALUATION OF
THE /-EXPONENT 174 5.7 COMPARISON OF DIFFERENT RG APPROACHES 176 6 RG
STUDY OF PARTICULAR SYSTEMS 179 6.1 REDUCTION OF THE CHARACTERISTIC SET
179 6.2 THE GAUSSIAN MODEL 182 6.3 THE * 4 MODEL 184 6.3.1 GENERAL
CONSIDERATION 184 6.3.2 0(N) SYMMETRY 190 6.3.3 CUBIC SYMMETRY 193 6.3.4
INTERACTING FIELDS 200 6.3.5 LOGARITHMICAL CORRECTIONS 207 6.4 THE * 4 +
/-MODEL 208 6.5 FREE ENERGY IN THE CRITICAL REGION 212 6.5.1 QUATRIC
FORM IN THE INSTABILITY REGION 212 6.5.2 CUBIC SYMMETRY 213 6.5.3
INTERACTING FIELDS 218 7 COMPETING INTERACTIONS 223 7.1 HEISENBERG
MAGNETS 223 7.1.1 RG EQUATIONS 224 7.1.2 FIXED POINTS 225 XIV CONTENTS
7.1.3 FLOW LINES AND PHASE DIAGRAMS 227 7.2 BICRITICAL POINTS IN
ANTIFERROMAGNETS 233 7.2.1 GINZBURG-LANDAU FUNCTIONAL 234 7.2.2 RG
ANALYSIS 236 7.2.3 EXPERIMENTAL DATA 240 7.3 DIPOLE INTERACTION 242
7.3.1 DIPOLE HAMILTONIAN 243 7.3.2 RG ANALYSIS 244 7.3.3 CUBIC SYMMETRY
245 7.3.4 TETRAGONAL SYMMETRY 247 7.4 IMPURE SYSTEMS 250 7.4.1 HARRIS S
CRITERION 253 7.4.2 THE REPLICA METHOD 254 7.4.3 RG ANALYSIS 256 7.4.4
FLOW LINE RUNAWAY 259 7.4.5 LOOP RENORMALIZATIONS 260 7.4.6 ANISOTROPIC
SYSTEMS 267 7.4.7 SYSTEMS WITH COMPETING INTERACTIONS 272 8 EXACTLY
SOLVABLE MODELS AND RG 287 8.1 FLUCTUATION EFFECTS IN SPHERICAL MODEL
287 8.1.1 INHOMOGENEOUS ORDERING 289 8.1.2 HOMOGENEOUS ORDERING 293 8.2
INVERSION OF PHASE TRANSITIONS 294 8.3 MODEL WITH REDUCED INTERACTION
301 8.3.1 GENERAL CONSIDERATION 301 8.3.2 CRITICAL EXPONENTS. CROSSOVER
306 8.4 FIRST-ORDER TRANSITIONS 308 8.4.1 CUBIC SYMMETRY 309 8.4.2
INTERACTING FIELDS 313 8.5 RG AND REDUCED INTERACTIONS 317 8.5.1 THE RG
EQUATION FOR THE MODEL 317 8.5.2 CRITICAL EXPONENTS 320 9 APPLICATION TO
COPPER OXIDES 323 9.1 INTRODUCTION 323 9.2 LA2CU0 4 SYSTEMS 324 9.2.1
THE GINZBURG-LANDAU FUNCTIONAL 327 9.2.2 MEAN FIELD APPROXIMATION 332
9.2.3 RG ANALYSIS 333 9.2.4 THE INFLUENCE OF IMPURITIES 337 9.3 OXYGEN
ORDERING IN *********+ * 338 CONTENTS XV 9.3.1 DESCRIPTION OF THE MODEL
340 9.3.2 FREE ENERGY 341 9.3.3 PHASE TRANSITION 344 9.3.4 CHANGE OF
OXYGEN CONCENTRATION 347 9.4 D-PAIRING IN THE SUPERCONDUCTING STATE 351
9.4.1 RG APPROACH 352 9.4.2 AN EXACTLY SOLVABLE MODEL 356 9.4.3
COMPARISON WITH RG 360 9.4.4 CONCLUSION 363 A EVALUATION OF INTEGRALS
365 A.L GAUSSIAN INTEGRAL 365 A.2 A TYPICAL DIAGRAM 366 * LOCAL RG 367
B.L GENERAL CONSIDERATION 367 B.2 SPECTRAL THEOREMS 369 B.3 LOCAL
EQUATION IN THE LIMIT M-»OO 371 BIBLIOGRAPHY 375 INDEX 387
|
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| id | DE-604.BV010540639 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:46Z |
| institution | BVB |
| isbn | 0387944141 |
| language | German |
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| physical | XV, 390 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Springer |
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| series2 | Graduate texts in contemporary physics |
| spelling | Ivančenko, Julij M. Verfasser aut Physics of critical fluctuations Yuli M. Ivanchenko ; Alexander A. Lisyansky New York [u.a.] Springer 1995 XV, 390 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in contemporary physics Literaturverz. S. 375 - 386 Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Fluktuation Physik (DE-588)4130671-5 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Fluktuation Physik (DE-588)4130671-5 s DE-604 Lisjanskij, Aleksandr A. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007026859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivančenko, Julij M. Lisjanskij, Aleksandr A. Physics of critical fluctuations Phasenumwandlung (DE-588)4132140-6 gnd Fluktuation Physik (DE-588)4130671-5 gnd |
| subject_GND | (DE-588)4132140-6 (DE-588)4130671-5 |
| title | Physics of critical fluctuations |
| title_auth | Physics of critical fluctuations |
| title_exact_search | Physics of critical fluctuations |
| title_full | Physics of critical fluctuations Yuli M. Ivanchenko ; Alexander A. Lisyansky |
| title_fullStr | Physics of critical fluctuations Yuli M. Ivanchenko ; Alexander A. Lisyansky |
| title_full_unstemmed | Physics of critical fluctuations Yuli M. Ivanchenko ; Alexander A. Lisyansky |
| title_short | Physics of critical fluctuations |
| title_sort | physics of critical fluctuations |
| topic | Phasenumwandlung (DE-588)4132140-6 gnd Fluktuation Physik (DE-588)4130671-5 gnd |
| topic_facet | Phasenumwandlung Fluktuation Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007026859&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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