Thermodynamics of one-dimensional solvable models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1999
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 252 S. graph. Darst. |
| ISBN: | 0521551439 9780521019798 9780521551434 |
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| 245 | 1 | 0 | |a Thermodynamics of one-dimensional solvable models |c Minoru Takahashi |
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| adam_text | THERMODYNAMICS OF ONE-DIMENSIONAL SOLVABLE MODELS MINORA TAKAHASHI
INSTITUTE FOR SOLID STATE PHYSICS, UNIVERSITY OF TOKYO, TOKYO, JAPAN *
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE XI PART ONE:
THERMODYNAMICS OF NON-INTERACTING SYSTEMS AND GROUND STATES OF
INTERACTING SYSTEMS 1 1 FREE ENERGY AND CORRELATION FUNCTIONS OF THE XY
MODEL 1 1.1 THE ISOTROPIC XY MODEL 1 1.1.1 INTRODUCTION AND HISTORICAL
OVERVIEW 1 1.1.2 ENERGY EIGENVALUES OF THE HAMILTONIAN AND THE PARTITION
FUNCTION 3 1.1.3 CORRELATION FUNCTIONS 4 1.2 THE ANISOTROPIC XY MODEL 7
1.2.1 THE SUBSPACE A = 1 8 1.2.2 THE SUBSPACE A = * 1 9 1.2.3 THE FREE
ENERGY 9 2 SYSTEMS WITH A DELTA-FUNCTION POTENTIAL 10 2.1 THE BOSON
PROBLEM 10 2.1.1 THE * = 0 CASE 10 2.1.2 THE * = OO CASE 11 2.1.3
SCATTERING STATES OF BOSE PARTICLES WITH FINITE INTERACTION 12 2.1.4
PERIODIC BOUNDARY CONDITIONS 14 2.1.5 LINEAR INTEGRAL EQUATION FOR THE
DISTRIBUTION OF QUASI-MOMENTA 15 2.1.6 BOUND STATES IN THE CASE * 0 16
2.1.7 ELEMENTARY EXCITATIONS FOR REPULSIVE BOSONS 18 2.2 THE FERMION
PROBLEM 20 2.2.1 THE * = 0 CASE 20 2.2.2 THE TWO-BODY PROBLEM 21 2.2.3
THE THREE-BODY PROBLEM 22 2.2.4 THE M = 1 AND ARBITRARY N CASE 25 2.2.5
THE ARBITRARY M AND N CASE 25 2.2.6 PERIODIC BOUNDARY CONDITIONS 26 V VI
CONTENTS 2.2.7 THE GROUND STATE FOR * 0 28 2.2.8 THE GROUND STATE FOR
* 0 29 2.2.9 EXPANSION FROM SMALL * 31 2.2.10 A UNIFIED FORM OF THE
INTEGRAL EQUATIONS 32 2.3 BOSONS AND FERMIONS WITH ARBITRARY SPIN 32 3
THE ISOTROPIC HEISENBERG MODEL 34 3.1 THE FERROMAGNETIC CASE 34 3.2 THE
STRING SOLUTION OF AN INFINITE SYSTEM 37 3.3 THE HULTHEN SOLUTION FOR AN
ANTIFERROMAGNET 37 3.4 THE DES CLOIZEAUX-PEARSON MODE OF AN
ANTIFERROMAGNET 39 3.5 THE MAGNETIC SUSCEPTIBILITY AND MAGNETIZATION
CURVE FOR J 0 41 3.6 WIENER-HOPF TYPE INTEGRAL EQUATION 44 4 THE XXZ
MODEL 4 6 4.1 SYMMETRY OF THE HAMILTONIAN 46 4.2 THE BETHE-ANSATZ WAVE
FUNCTION 47 4.3 THE STRING SOLUTION FOR A 1 48 4.4 THE LOWEST ENERGY
STATE FOR A * 1 49 4.5 THE MAGNETIZATION CURVE FOR A FIELD IN THE
Z-DIRECTION AT A * 1 51 4.6 THE LOWEST ENERGY STATE FOR FIXED M AND *
1 A 1 52 4.7 THE MAGNETIZATION CURVE FOR A FIELD IN THE Z-DIRECTION
AT -1 A 1 53 4.8 SUSCEPTIBILITY FOR -1 A 1 54 4.9 THE LONG RANGE
ORDER OF THE XXZ MODEL 56 4.10 EXCITATIONS FROM THE GROUND STATE 59
4.10.1 A * 1 AND THE ENERGY GAP 59 4.10.2 EXCITATIONS FOR -1 A 1
61 4.10.3 SPIN-WAVE LIKE EXCITATIONS FOR 0 A 1 62 4.10.4 THE
SPIN-WAVE BOUND STATE 64 5 XYZ AND EIGHT-VERTEX MODELS 67 5.1 TRANSFER
MATRIX OF THE EIGHT-VERTEX MODEL 67 5.1.1 RELATION BETWEEN THE
SIX-VERTEX MODEL AND THE XXZ MODEL 67 5.1.2 THE EIGHT-VERTEX MODEL AND
THE XYZ MODEL 70 5.2 THE SYMMETRY OF THE XYZ MODEL 73 5.3 MODULUS / AND
MODULUS * 74 5.4 THE CASE J X = 0 76 5.5 THE GROUND STATE FOR J Z 0 77
5.6 LONG RANGE ORDER 79 5.7 ELEMENTARY EXCITATIONS 80 5.7.1 THE NEARLY
DEGENERATE GROUND STATE 80 5.7.2 SPINON EXCITATIONS 80 CONTENTS VII
5.7.3 SPIN-WAVE EXCITATIONS 81 5.7.4 SPIN-WAVE BOUND STATES 83 6 THE
HUBBARD MODEL 85 6.1 SYMMETRY OF THE HAMILTONIAN 85 6.1.1 PARTICLE-HOLE
SYMMETRY 85 6.1.2 SU(2) SYMMETRY 87 6.2 THE BETHE-ANSATZ EQUATION FOR
THE ONE-DIMENSIONAL HUBBARD MODEL 88 6.2.1 THE WAVE FUNCTION FOR A
FINITE SYSTEM 88 6.2.2 PERIODIC BOUNDARY CONDITION 90 6.2.3 FREDHOLM
TYPE INTEGRAL EQUATIONS FOR THE GROUND STATE 90 6.2.4 ANALYTIC SOLUTION
FOR THE GROUND STATE IN THE HALF-FILLED CASE 92 6.2.5 SPINON EXCITATION
IN THE HALF-FILLED CASE 92 6.2.6 ENERGY GAP OF THE CHARGE EXCITATION 95
6.2.7 SUSCEPTIBILITY AND MAGNETIZATION CURVE OF THE HALF-FILLED CASE 97
6.3 1/17 EXPANSION 101 6.4 PERTURBATION EXPANSION IN THE HALF-FILLED
CASE 102 6.5 ASYMPTOTIC EXPANSION FROM U = 0 104 PART TWO: FINITE
TEMPERATURE INTEGRAL EQUATIONS FOR UN-NESTED SYSTEMS 109 7 REPULSIVE
DELTA-FUNCTION BOSONS 109 7.1 UNIQUENESS OF THE SOLUTION 109 7.2 HOLES
OF QUASI-MOMENTA AND THEIR DISTRIBUTION FUNCTION 110 7.3 THERMODYNAMIC
EQUILIBRIUM 111 7.4 ELEMENTARY EXCITATIONS 113 7.5 SOME SPECIAL LIMITS
115 7.5.1 THE * = OO LIMIT 115 7.5.2 THEC = 0+ LIMIT 116 7.5.3 THE T =
0+LIMIT 116 8 THERMODYNAMICS OF THE XXX CHAIN 117 8.1 STRING SOLUTION OF
AN INFINITE XXX CHAIN 117 8.2 STRING HYPOTHESIS FOR A LONG XXX CHAIN 118
8.3 THERMODYNAMIC BETHE-ANSATZ EQUATIONS FOR THE XXX CHAIN 120 8.4 SOME
SPECIAL CASES AND EXPANSIONS 123 8.4.1 THE J/T -» 0 CASE 123 8.4.2
HIGH-TEMPERATURE EXPANSION OR SMALL J EXPANSION 124 8.4.3 THE
LOW-TEMPERATURE LIMIT 126 8.4.4 THE FUGACITY EXPANSION 127 9
THERMODYNAMICS OF THE XXZ MODEL 130 9.1 THERMODYNAMIC EQUATIONS FOR THE
XXZ MODEL FOR A 1 130 VLLL CONTENTS 9.2 THEORY FOR THE |A| 1 XXZ
MODEL 133 9.2.1 STRING SOLUTION OF THE INFINITE XXZ MODEL WITH |A| 1
133 9.2.2 SCATTERING PHASE SHIFT AMONG STRINGS 138 9.2.3 BETHE-ANSATZ
EQUATION FOR THE XXZ MODEL WITH |A| 1 139 9.3 SOME SPECIAL LIMITS 143
9.3.1 THE T -+ OO OR J -+ 0 LIMIT 143 9.3.2 THE CASE J 0, -1 A 0
AND T -* 0 144 9.3.3 THE CASE J 0, 0 A 1 AND T - 0 144 9.3.4 THE
A = 0 CASE 144 10 THERMODYNAMICS OF THE XYZ MODEL 145 10.1 BETHE-ANSATZ
EQUATION FOR THE XYZ MODEL 145 10.2 SOME SPECIAL LIMITS 149 10.2.1 THE T
-* OO OR J -* 0 LIMIT 149 10.2.2 THE J Z 0, J X 0 AND T -* 0 LIMIT
150 10.2.3 THE J Z 0, J X 0 AND T -» 0 LIMIT 150 10.2.4 THE J X = 0
CASE 151 11 LOW-TEMPERATURE THERMODYNAMICS 152 11.1 THE XXZ MODEL 152
11.1.1 THE XXZ MODEL AT 2A J(L - A), A 1 152 11.1.2 THE CASE 7(1 -
A)/2 H 0 152 11.2 ROGER S DILOGARITHM AND SPECIFIC HEAT AT H = 0 153
11.2.1 SPECIFIC HEAT OF THE XXX ANTIFERROMAGNET 153 11.3 THE
FERROMAGNETIC CHAIN AND MODIFIED SPIN-WAVE THEORY 155 11.3.1 NUMERICAL
ANALYSIS OF THE THERMODYNAMIC BETHE-ANSATZ EQUATION 155 11.3.2 SPIN-WAVE
CALCULATION OF THE ID FERROMAGNETIC CHAIN 155 11.4 THE ANTIFERROMAGNETIC
XXX MODEL 156 11.5 THE XYZ MODEL AT J X J Y J Z 157 PART THREE:
FINITE TEMPERATURE INTEGRAL EQUATIONS FOR NESTED SYSTEMS 159 12 S = 1/2
FERMIONS WITH REPULSIVE POTENTIAL IN THE CONTINUUM 159 12.1 DERIVATION
OF THE THERMODYNAMIC EQUATIONS 159 12.2 SOME SPECIAL LIMITS 164 12.2.1
C^0+ 164 12.2.2 *-** 166 13 S = 1/2 FERMIONS WITH AN ATTRACTIVE
POTENTIAL 167 13.1 DERIVATION OF THE THERMODYNAMIC EQUATIONS 167 13.2
SOME SPECIAL LIMITS 171 13.2.1 C^0- 171 13.2.2 T- 0+ 172 CONTENTS IX 14
THERMODYNAMICS OF THE HUBBARD MODEL 174 14.1 STRINGS OF THE HUBBARD
MODEL 174 14.2 THERMODYNAMIC BETHE-ANSATZ EQUATION FOR THE HUBBARD MODEL
177 14.3 SOME SPECIAL LIMITS 179 14.3.1 THE LIMIT U -» OO 179 14.3.2 THE
LIMIT U -* 0 180 14.3.3 THE LIMIT T - 0 182 14.3.4 THE LIMIT T - » 0
183 PART FOUR: THE QUANTUM TRANSFER MATRIX AND RECENT DEVELOPMENTS 185
15 THE TRANSFER MATRIX AND CORRELATION LENGTH 185 15.1 THE TRANSFER
MATRIX FOR THE ISING CHAIN 185 15.2 THE TRANSFER MATRIX FOR THE
CLASSICAL HEISENBERG MODEL 186 16 THE SPIN 1/2 XXZ MODEL IN A MAGNETIC
FIELD 189 16.1 THE DIAGONAL-TO-DIAGONAL TRANSFER MATRIX 189 16.2 THE
LIMIT OF AN INFINITE TROTTER NUMBER 198 16.3 ANALYTICAL SOLUTIONS FOR
SPECIAL CASES 201 16.3.1 THE ISING LIMIT 201 16.3.2 THE XY LIMIT 202
16.3.3 THE T = H = 0 CASE 203 16.4 NUMERICAL CALCULATIONS OF THE XXZ
MODEL 205 17 THE XYZ MODEL WITH NO MAGNETIC FIELD 210 17.1 THE TRANSFER
MATRIX FOR THE XYZ MODEL 210 17.1.1 BAXTER S THEORY FOR THE
INHOMOGENEOUS EIGHT-VERTEX MODEL 211 17.1.2 TRANSCENDENTAL EQUATIONS 212
17.1.3 THE LIMIT OF M - OO 215 17.2 SPECIAL CASES AND NUMERICAL METHODS
218 17.2.1 THE T - 0 LIMIT 218 17.2.2 THE J X * 0 CASE (ANISOTROPIC XY
CHAIN) 220 17.3 NUMERICAL CALCULATIONS 221 18 RECENT DEVELOPMENTS AND
RELATED TOPICS 223 18.1 NUMERICAL ANALYSIS OF THE S = 1 CHAIN 223
APPENDIX A THE YOUNG TABLEAU AND THE THEOREM OF LIEB AND MATTIS 226
APPENDIX * THE NUMBER OF STRING SOLUTIONS 228 APPENDIX * THE COMMUTING
TRANSFER MATRIX AND SPECTRAL PARAMETER 231 APPENDIX D THE MATRIX Q(V)
235 APPENDIX E SPECIAL FUNCTIONS 239 BIBLIOGRAPHY 246 INDEX 251
|
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| author_facet | Takahashi, Minoru 1944- |
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| discipline | Physik |
| edition | 1. publ. |
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| indexdate | 2024-07-09T18:33:16Z |
| institution | BVB |
| isbn | 0521551439 9780521019798 9780521551434 |
| language | English |
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| physical | XIII, 252 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
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| spelling | Takahashi, Minoru 1944- Verfasser (DE-588)172894220 aut Thermodynamics of one-dimensional solvable models Minoru Takahashi 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1999 XIII, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Física matemática Termodinámica estadística Técnica Bethe-ansatz Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008680558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Takahashi, Minoru 1944- Thermodynamics of one-dimensional solvable models Física matemática Termodinámica estadística Técnica Bethe-ansatz Statistische Thermodynamik (DE-588)4126251-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4126251-7 (DE-588)4114528-8 |
| title | Thermodynamics of one-dimensional solvable models |
| title_auth | Thermodynamics of one-dimensional solvable models |
| title_exact_search | Thermodynamics of one-dimensional solvable models |
| title_full | Thermodynamics of one-dimensional solvable models Minoru Takahashi |
| title_fullStr | Thermodynamics of one-dimensional solvable models Minoru Takahashi |
| title_full_unstemmed | Thermodynamics of one-dimensional solvable models Minoru Takahashi |
| title_short | Thermodynamics of one-dimensional solvable models |
| title_sort | thermodynamics of one dimensional solvable models |
| topic | Física matemática Termodinámica estadística Técnica Bethe-ansatz Statistische Thermodynamik (DE-588)4126251-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Física matemática Termodinámica estadística Técnica Bethe-ansatz Statistische Thermodynamik Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008680558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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