Locating the Ising CFT via the ground-state energy on the fuzzy sphere
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908624242081792 |
|---|---|
| author | Wiese, Kay Joerg |
| author_facet | Wiese, Kay Joerg |
| contents | We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ...$, and to search for a minimum of $ χ:=E_{3/2}/E_0$ as a function of the couplings. Conformal perturbation theory predicts that around a CFT, $χ= χ_{\rm min} + \sum_i λ_i^2 N_m^{-ω_i} + O(λ^3)$, where $λ_i$ are the couplings associated to perturbations of operators with dimension $Δ_i$, and $ω_i = d-Δ_i$. This procedure finds the critical curve of [PRX 13 (2023) 021009] and their sweet spot with good precision. Varying two coupling constants allows us to extract the correction-to-scaling exponent $ω$ associated to the two leading scalars $ε$, and $ε'$. We find similar results when normalizing by the gap to the stress tensor $T$ or first parity-odd operator $σ$ instead of $E_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locating the Ising CFT via the ground-state energy on the fuzzy sphere Wiese, Kay Joerg High Energy Physics - Theory Statistical Mechanics We locate the phase-transition line for the Ising model on the fuzzy sphere from a finite-size scaling analysis of its ground-state energy. Our strategy is to write the latter as $E_{GS}(N_m)/N_m = E_{0} + E_1 /N_m + E_{3/2}/N_m^{3/2}+ ...$, and to search for a minimum of $ χ:=E_{3/2}/E_0$ as a function of the couplings. Conformal perturbation theory predicts that around a CFT, $χ= χ_{\rm min} + \sum_i λ_i^2 N_m^{-ω_i} + O(λ^3)$, where $λ_i$ are the couplings associated to perturbations of operators with dimension $Δ_i$, and $ω_i = d-Δ_i$. This procedure finds the critical curve of [PRX 13 (2023) 021009] and their sweet spot with good precision. Varying two coupling constants allows us to extract the correction-to-scaling exponent $ω$ associated to the two leading scalars $ε$, and $ε'$. We find similar results when normalizing by the gap to the stress tensor $T$ or first parity-odd operator $σ$ instead of $E_0$. |
| title | Locating the Ising CFT via the ground-state energy on the fuzzy sphere |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2510.09482 |