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Conformal Invariance in Statistical and Condensed Matter Physics.
Conformal Invariance in Statistical and Condensed Matter Physics.
상세정보
- 자료유형
- 학위논문
- Control Number
- 0017165172
- International Standard Book Number
- 9798346852513
- Dewey Decimal Classification Number
- 530
- Main Entry-Personal Name
- Padayasi, Jaychandran.
- Publication, Distribution, etc. (Imprint
- [S.l.] : The Ohio State University., 2024
- Publication, Distribution, etc. (Imprint
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- Physical Description
- 137 p.
- General Note
- Source: Dissertations Abstracts International, Volume: 86-06, Section: B.
- General Note
- Advisor: Gruzberg, Ilya.
- Dissertation Note
- Thesis (Ph.D.)--The Ohio State University, 2024.
- Summary, Etc.
- 요약Phase transitions occur in many classical and quantum systems, and are the subject of many an open problem in physics. In the past decade, the conformal bootstrap has provided new perspectives for looking at the critical point of a transition. With this formalism, it is possible to exploit the conformal symmetry intrinsically present at the critical point, and derive general results about classes of transitions that obey the same symmetries. This thesis presents the application of this method to two problems of note in classical and quantum phase transitions.The first is a classical model of O(N) spins in the presence of a boundary. We use the numerical conformal bootstrap to prove rigorously the existence of a new boundary phase in three-dimensional Heisenberg (O(3)) and O(4) magnets, deemed the extraordinary-log universality class. The results agree well with a parallel numerical study but are more rigorous due to the bounded nature of the error.The second case is the inherently quantum problem of Anderson transitions between metals and insulators. It has been discovered that at criticality, the wavefunctions describe multifractal objects, that are described by infinitely many fractal dimensions. We use analytical constraints from conformal symmetry to predict the form of these fractal parameters in dimensions greater than two. Our exact prediction, which works in arbitrary dimensions, can be used as a probe for conformal symmetry at Anderson transitions.By studying these two problems, we demonstrate the power of conformal symmetry as a non-perturbative tool in the theory of phase transitions in arbitrary dimensions. Throughout the thesis, we have extended the domain of applicability of traditional bootstrap techniques for the purpose of non-unitary and non-positive systems.
- Subject Added Entry-Topical Term
- Physics.
- Subject Added Entry-Topical Term
- Condensed matter physics.
- Subject Added Entry-Topical Term
- Statistical physics.
- Subject Added Entry-Topical Term
- Quantum physics.
- Index Term-Uncontrolled
- Phase transitions
- Index Term-Uncontrolled
- Conformal invariance
- Index Term-Uncontrolled
- Critical phenomena
- Index Term-Uncontrolled
- Quantum phase transitions
- Added Entry-Corporate Name
- The Ohio State University Physics
- Host Item Entry
- Dissertations Abstracts International. 86-06B.
- Electronic Location and Access
- 로그인을 한후 보실 수 있는 자료입니다.
- Control Number
- joongbu:655047
MARC
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aPadayasi, Jaychandran.
■24510▼aConformal Invariance in Statistical and Condensed Matter Physics.
■260 ▼a[S.l.]▼bThe Ohio State University. ▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a137 p.
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-06, Section: B.
■500 ▼aAdvisor: Gruzberg, Ilya.
■5021 ▼aThesis (Ph.D.)--The Ohio State University, 2024.
■520 ▼aPhase transitions occur in many classical and quantum systems, and are the subject of many an open problem in physics. In the past decade, the conformal bootstrap has provided new perspectives for looking at the critical point of a transition. With this formalism, it is possible to exploit the conformal symmetry intrinsically present at the critical point, and derive general results about classes of transitions that obey the same symmetries. This thesis presents the application of this method to two problems of note in classical and quantum phase transitions.The first is a classical model of O(N) spins in the presence of a boundary. We use the numerical conformal bootstrap to prove rigorously the existence of a new boundary phase in three-dimensional Heisenberg (O(3)) and O(4) magnets, deemed the extraordinary-log universality class. The results agree well with a parallel numerical study but are more rigorous due to the bounded nature of the error.The second case is the inherently quantum problem of Anderson transitions between metals and insulators. It has been discovered that at criticality, the wavefunctions describe multifractal objects, that are described by infinitely many fractal dimensions. We use analytical constraints from conformal symmetry to predict the form of these fractal parameters in dimensions greater than two. Our exact prediction, which works in arbitrary dimensions, can be used as a probe for conformal symmetry at Anderson transitions.By studying these two problems, we demonstrate the power of conformal symmetry as a non-perturbative tool in the theory of phase transitions in arbitrary dimensions. Throughout the thesis, we have extended the domain of applicability of traditional bootstrap techniques for the purpose of non-unitary and non-positive systems.
■590 ▼aSchool code: 0168.
■650 4▼aPhysics.
■650 4▼aCondensed matter physics.
■650 4▼aStatistical physics.
■650 4▼aQuantum physics.
■653 ▼aPhase transitions
■653 ▼aConformal invariance
■653 ▼aCritical phenomena
■653 ▼aQuantum phase transitions
■690 ▼a0611
■690 ▼a0605
■690 ▼a0599
■690 ▼a0217
■71020▼aThe Ohio State University▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-06B.
■790 ▼a0168
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17165172▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
