컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0129 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | (PS) Probability and Statistics (PS) |
| 발표시간(Time) | 20th-C-10:20 -- 10:40 |
| 영문제목 (Title(Eng.)) |
Finite-size scaling and plateau for the hierarchical $\phi^4$ model in dimension $\ge 4$ |
| 저자(Author(s)) |
Jiwoon Park1, Gordon Slade2 Korea Air Force Academy1, University of British Columbia2 |
| 초록본문(Abstract) | Finite-size scaling investigates how critical exponents are affected by finite system sizes and boundary effects. Despite its roots tracing back to the seminal work of Fisher et al. (1971), the field has maintained its relevance due to its distinct characteristics compared to infinite volume theories. One notable phenomenon within finite-size scaling is the plateau effect, observed when the correlation function reaches a constant value within a torus geometry, which provides valuable insights into the behavior of critical systems under confinement. In parallel, the $\phi^4$ model serves as a cornerstone in statistical field theory, offering insights into critical phenomena observed in various systems, such as spin models and self-avoiding walks. Particularly in dimensions greater than or equal to 4 at the critical point, the $\phi^4$ model exhibits a Gaussian infrared limit, a key property that underpins its relevance in understanding critical behavior. However, despite extensive research, the precise role of boundary conditions and finite-size scaling in this context remains elusive. To address this challenge, we focus our attention on the hierarchical $\phi^4$ model, a simplified toy model designed to facilitate renormalisation group analysis. With this simplification, we aim to provide a clearer understanding of the exact critical exponents, including logarithmic corrections, and verify the presence of plateau effects within the critical window, shedding light on the intricate interplay between finite size effects and critical phenomena in the $\phi^4$ model. |
| 분류기호 (MSC number(s)) |
82B27, 82B28, 60K35 |
| 키워드(Keyword(s)) | $\phi^4$ model, plateau, renormalisation group |
| 강연 형태 (Language of Session (Talk)) |
Korean |