자료유형  

 학위논문

Control Number  

0017164282

International Standard Book Number  

9798342136303

Dewey Decimal Classification Number  

500

Main Entry-Personal Name  

Yuan, Andrew Chang.

Publication, Distribution, etc. (Imprint  

[S.l.] : Stanford University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

121 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

General Note  

Advisor: Kivelson, Steven.

Dissertation Note  

Thesis (Ph.D.)--Stanford University, 2024.

Summary, Etc.  

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.

Subject Added Entry-Topical Term  

Decomposition.

Subject Added Entry-Topical Term  

Phase transitions.

Subject Added Entry-Topical Term  

Physics.

Subject Added Entry-Topical Term  

Probability distribution.

Subject Added Entry-Topical Term  

Symmetry.

Subject Added Entry-Topical Term  

Statistics.

Added Entry-Corporate Name  

Stanford University.

Host Item Entry  

Dissertations Abstracts International. 86-04B.

Electronic Location and Access  

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Control Number  

joongbu:655559