Strongly disordered quantum spin systems in low dimensions: numerical study of spin chains, spin ladders and two-dimensional systems
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Jülich
John-von-Neumann-Inst. für Computing
2002
|
| Series: | NIC-Serie
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 128 S. graph. Darst. : 24 cm |
| ISBN: | 3000090568 |
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| 100 | 1 | |a Lin, Yu-cheng |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Strongly disordered quantum spin systems in low dimensions |b numerical study of spin chains, spin ladders and two-dimensional systems |c Yu-cheng Lin |
| 264 | 1 | |a Jülich |b John-von-Neumann-Inst. für Computing |c 2002 | |
| 300 | |a IV, 128 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a NIC-Serie |v 12 | |
| 502 | |a Zugl.: Köln, Univ., Diss., 2001 | ||
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| adam_text |
CONTENTS
1
INTRODUCTION
TO
QUANTUM
PHASE
TRANSITIONS
WITH
DISORDER
1
1.1
CONTINUOUS
QUANTUM
PHASE
TRANSITIONS
.
2
1.2
THE
PATH-INTEGRAL
FORMULATION
OF
THE
QUANTUM
STATISTICAL
MECHANICS
.
2
1.3
EXAMPLES
OF
QUANTUM
PHASE
TRANSITIONS
.
4
1.4
EFFECTS
OF
QUENCHED
RANDOMNESS
ON
QUANTUM
PHASE
TRANSITIONS
.
6
1.4.1
GRIFFITHS-MCCOY
SINGULARITIES
.
6
1.4.2
ACTIVATED
DYNAMIC
SCALING
.
9
1.5
EXACT
RESULTS
OF
THE
RANDOM
TRANSVERSE-FIELD
ISING
FERROMAGNETIC CHAIN
.
.
10
2
CONTINUOUS-TIME
CLUSTER
ALGORITHM
FOR
QUANTUM
MONTE
CARLO
SIMULATIONS
15
2.1
QUANTUM-CLASSICAL
MAPPING
OF
THE
TRANSVERSE
ISING
MODEL
.
15
2.2
THE
CONTINUOUS-IMAGINARY-TIME
CLUSTER
ALGORITHM
.
18
2.2.1
MOTIVATION
.
18
2.2.2
DESCRIPTION
OF
THE
ALGORITHM
.
18
3
MONTE
CARLO
SIMULATIONS
OF
THE
TRANSVERSE
ISING
MODEL
21
3.1
MEASUREMENTS
AND
ANISOTROPIC
FINITE
SIZE
SCALING
.
21
3.2
PURE
SYSTEMS
IN
ONE
AND
TWO
DIMENSIONS
.
24
3.3
RANDOM SYSTEMS
IN
ONE
AND
TWO
DIMENSIONS
.
27
3.3.1
THE
ONE-DIMENSIONAL
CASE
.
27
3.3.2
THE
TWO-DIMENSIONAL
CASE
.
34
CONTENTS
4
THE
MA-DASGUPTA-HU RENORMALIZATION-GROUP
METHOD
41
4.1
OVERVIEW
.
41
4.2
THE
MDH
RG
FOR
TRANSVERSE-FIELD
ISING
CHAINS
.
42
4.2.1
THE
RENORMALIZATION-GROUP
SCHEME
IN
ONE
DIMENSION
.
42
4.2.2
RENORMALIZATION-GROUP
FLOWS
IN
ONE
DIMENSION
.
44
4.2.2.1
THE
RG
FLOWS
IN
THE
VICINITY
OF
THE
CRITICAL
POINT
.
45
4.2.2.2
THE
RG
FLOWS
IN
THE
GRIFFITHS-MCCOY
REGIONS
.
46
4.3
THE
MDH
RG
FOR
XX
AND
HEISENBERG
CHAINS
.
47
4.3.1
THE
RENORMALIZATION-GROUP
PROCEDURE
.
48
4.3.2
THE
ANALYTICAL
RESULTS
.
49
5
NUMERICAL
RENORMALIZATION-GROUP
STUDY
OF
RANDOM
TRANSVERSE
ISING
MOD
ELS
53
5.1
THE
NUMERICAL
RG
SCHEME
IN
HIGHER
DIMENSIONS
.
53
5.2
THE
ONE-DIMENSIONAL
MODEL
.
57
5.3
THE
DOUBLE
CHAIN
.
61
5.4
THE
SQUARE
LATTICE
.
67
5.5
SUMMARY
AND
CONCLUSIONS
.
71
6
RANDOM QUANTUM MAGNETS WITH
BROAD
DISORDER
DISTRIBUTION
75
6.1
INTRODUCTION
.
75
6.2
THE
ONE-DIMENSIONAL
PROBLEM
.
77
6.2.1
EXACT
RESULTS
THROUGH
A
MAPPING
TO
RANDOM
WALKS
.
T1
6.2.2
BULK
MAGNETIZATION:
A
NUMERICAL
RENORMALIZATION GROUP
STUDY
.
.
80
6.3
THE
TWO-DIMENSIONAL
PROBLEM
.
83
6.4
SUMMARY
.
86
7
STRONGLY
DISORDERED
SPIN
LADDERS
89
7.1
INTRODUCTION
.
89
7.2
THE
MODELS
AND
THEIR
PHASE
DIAGRAMS
FOR
NON-RANDOM
COUPLINGS
.
90
7.3
RENORMALIZATION
PROCEDURE
FOR
ANTIFERROMAGNETIC
SPIN
LADDERS
.
94
7.4
RESULTS
.
97
7.4.1
RANDOM
CONVENTIONAL
LADDERS
.
97
II
CONTENTS
7.4.2
RANDOM
LADDERS
WITH
STAGGERED
DIMERIZATION
.
99
7.4.3
RANDOM
ZIG-ZAG
LADDERS
.
102
7.4.4
RANDOM
JI-J?
LADDERS
.
104
7.5
DISCUSSION
.
106
8
SUMMARY
109
APPENDIX:
SURVIVING
PROBABILITY
OF
LEVY
FLIGHTS
113
ACKNOWLEDGMENTS
123
ZUSAMMENFASSUNG
125
III |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV014257414 |
| illustrated | Illustrated |
| indexdate | 2025-03-10T11:07:26Z |
| institution | BVB |
| isbn | 3000090568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009777292 |
| oclc_num | 50459912 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-188 |
| physical | IV, 128 S. graph. Darst. : 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | John-von-Neumann-Inst. für Computing |
| record_format | marc |
| series | NIC-Serie |
| series2 | NIC-Serie |
| spelling | Lin, Yu-cheng Verfasser aut Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems Yu-cheng Lin Jülich John-von-Neumann-Inst. für Computing 2002 IV, 128 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier NIC-Serie 12 Zugl.: Köln, Univ., Diss., 2001 Hochschulschrift gtt Niederdimensionales System (DE-588)4202325-7 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Quantenspinsystem (DE-588)4609091-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantenspinsystem (DE-588)4609091-5 s Ungeordnetes System (DE-588)4124353-5 s Niederdimensionales System (DE-588)4202325-7 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 NIC-Serie 12 (DE-604)BV013326983 12 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009777292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lin, Yu-cheng Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems NIC-Serie Hochschulschrift gtt Niederdimensionales System (DE-588)4202325-7 gnd Ungeordnetes System (DE-588)4124353-5 gnd Quantenspinsystem (DE-588)4609091-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4202325-7 (DE-588)4124353-5 (DE-588)4609091-5 (DE-588)4128130-5 (DE-588)4113937-9 |
| title | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems |
| title_auth | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems |
| title_exact_search | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems |
| title_full | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems Yu-cheng Lin |
| title_fullStr | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems Yu-cheng Lin |
| title_full_unstemmed | Strongly disordered quantum spin systems in low dimensions numerical study of spin chains, spin ladders and two-dimensional systems Yu-cheng Lin |
| title_short | Strongly disordered quantum spin systems in low dimensions |
| title_sort | strongly disordered quantum spin systems in low dimensions numerical study of spin chains spin ladders and two dimensional systems |
| title_sub | numerical study of spin chains, spin ladders and two-dimensional systems |
| topic | Hochschulschrift gtt Niederdimensionales System (DE-588)4202325-7 gnd Ungeordnetes System (DE-588)4124353-5 gnd Quantenspinsystem (DE-588)4609091-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Hochschulschrift Niederdimensionales System Ungeordnetes System Quantenspinsystem Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009777292&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013326983 |
| work_keys_str_mv | AT linyucheng stronglydisorderedquantumspinsystemsinlowdimensionsnumericalstudyofspinchainsspinladdersandtwodimensionalsystems |