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Phase Transitions in Multicomponent Systems
Phase Transitions in Multicomponent Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152943
- ISBN
- 9798342136303
- DDC
- 500
- 서명/저자
- Phase Transitions in Multicomponent Systems
- 발행사항
- [Sl] : Stanford University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 121 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
- 주기사항
- Advisor: Kivelson, Steven.
- 학위논문주기
- Thesis (Ph.D.)--Stanford University, 2024.
- 초록/해제
- 요약Phase transitions are typically characterized by the spontaneous symmetry breaking (SSB) of the symmetry group at low temperatures in contrast to the proliferation of topological defects at high temperatures. The most famous example would be the Ising model possessing a Z2 symmetry. At low temperatures (and in d ≥ 2 dimensions), the Ising model orders in the sense that the macroscopic properties of the system are sensitive to boundary conditions; notably, the magnetization will order in the same direction as the boundary spins, thereby exhibiting SSB in Z2. Conversely, at high temperatures, the system is disordered evidenced by the vanishing average magnetization irrespective of boundary conditions.In multi-component systems, the symmetry group are generally decomposable G x H, thus indicating the possibility of multiple phase transitions corresponding to the SSB of each subgroup G and H. Despite the simple algebraic structure of the symmetry group G x H, the local degrees of freedom can interact in a nontrivial manner, resulting in a nontrivial phase diagram than cannot be easily predicted from understanding the single component systems separately. Notably, it raises the question whether there exists a general approach in understanding and predicting the phase diagram of multicomponent systems.In this work, we will report some progress in understanding the physics of such systems by providing exact results. In Chapter (2), we will discuss the primary motivation of multi-component systems considered in this manuscript. In particular, we will consider two distinct classes of U(1)xZ2 Hamiltonians, where SSB in U(1) corresponds to the superconducting (SC) transition and SSB in Z2 corresponds to time-reversal symmetry breaking (TRSB). In Chapter (3), we discuss the first class where TRSB is induced by quenched disorder possessing Z2 symmetry. We construct an exactly solvable model which exhibits features resembling mean-field theory, within the context of which, we prove rigorously that despite possessing a decomposable symmetry group, there is only a single phase transition with a transition temperature independent of the disorder strength, implying that disorder can induce infinitely stableordering even at large disorder strength. In Chapter (4), we discuss the second class, where TRSB is innately induced by higher order Josephson interactions. We go beyond mean-field theory and develop an exact cluster representation of the system on any graphical structure (e.g., Z d for all d ≥ 1) by borrowing insights from FK-percolation within the Ising model. In particular, the cluster representation permits us to prove rigorously that TRSB transition must occur at an equal or higher temperature than the SC transition. Finally, in Chapter (5), we conclude by addressing the possible implications of our results and its relation to other multi-component systems.
- 일반주제명
- Decomposition
- 일반주제명
- Phase transitions
- 일반주제명
- Physics
- 일반주제명
- Probability distribution
- 일반주제명
- Symmetry
- 일반주제명
- Statistics
- 기타저자
- Stanford University.
- 기본자료저록
- Dissertations Abstracts International. 86-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017164282
■00520250211152943
■006m o d
■007cr#unu||||||||
■020 ▼a9798342136303
■035 ▼a(MiAaPQ)AAI31591772
■035 ▼a(MiAaPQ)Stanfordbw377hf4205
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a500
■1001 ▼aYuan, Andrew Chang.
■24510▼aPhase Transitions in Multicomponent Systems
■260 ▼a[Sl]▼bStanford University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a121 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-04, Section: B.
■500 ▼aAdvisor: Kivelson, Steven.
■5021 ▼aThesis (Ph.D.)--Stanford University, 2024.
■520 ▼aPhase transitions are typically characterized by the spontaneous symmetry breaking (SSB) of the symmetry group at low temperatures in contrast to the proliferation of topological defects at high temperatures. The most famous example would be the Ising model possessing a Z2 symmetry. At low temperatures (and in d ≥ 2 dimensions), the Ising model orders in the sense that the macroscopic properties of the system are sensitive to boundary conditions; notably, the magnetization will order in the same direction as the boundary spins, thereby exhibiting SSB in Z2. Conversely, at high temperatures, the system is disordered evidenced by the vanishing average magnetization irrespective of boundary conditions.In multi-component systems, the symmetry group are generally decomposable G x H, thus indicating the possibility of multiple phase transitions corresponding to the SSB of each subgroup G and H. Despite the simple algebraic structure of the symmetry group G x H, the local degrees of freedom can interact in a nontrivial manner, resulting in a nontrivial phase diagram than cannot be easily predicted from understanding the single component systems separately. Notably, it raises the question whether there exists a general approach in understanding and predicting the phase diagram of multicomponent systems.In this work, we will report some progress in understanding the physics of such systems by providing exact results. In Chapter (2), we will discuss the primary motivation of multi-component systems considered in this manuscript. In particular, we will consider two distinct classes of U(1)xZ2 Hamiltonians, where SSB in U(1) corresponds to the superconducting (SC) transition and SSB in Z2 corresponds to time-reversal symmetry breaking (TRSB). In Chapter (3), we discuss the first class where TRSB is induced by quenched disorder possessing Z2 symmetry. We construct an exactly solvable model which exhibits features resembling mean-field theory, within the context of which, we prove rigorously that despite possessing a decomposable symmetry group, there is only a single phase transition with a transition temperature independent of the disorder strength, implying that disorder can induce infinitely stableordering even at large disorder strength. In Chapter (4), we discuss the second class, where TRSB is innately induced by higher order Josephson interactions. We go beyond mean-field theory and develop an exact cluster representation of the system on any graphical structure (e.g., Z d for all d ≥ 1) by borrowing insights from FK-percolation within the Ising model. In particular, the cluster representation permits us to prove rigorously that TRSB transition must occur at an equal or higher temperature than the SC transition. Finally, in Chapter (5), we conclude by addressing the possible implications of our results and its relation to other multi-component systems.
■590 ▼aSchool code: 0212.
■650 4▼aDecomposition
■650 4▼aPhase transitions
■650 4▼aPhysics
■650 4▼aProbability distribution
■650 4▼aSymmetry
■650 4▼aStatistics
■690 ▼a0605
■690 ▼a0463
■71020▼aStanford University.
■7730 ▼tDissertations Abstracts International▼g86-04B.
■790 ▼a0212
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17164282▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
