Large N Limit of the O(N) Linear Sigma Model in 3D
文献类型：期刊论文
| 作者 | Shen, Hao3; Zhu, Rongchan1; Zhu, Xiangchan2
|
| 刊名 | COMMUNICATIONS IN MATHEMATICAL PHYSICS
 |
| 出版日期 | 2022-06-16 |
| 页码 | 57 |
| ISSN号 | 0010-3616 |
| DOI | 10.1007/s00220-022-04414-w |
| 英文摘要 | In this paper we study the large N limit of the O( N)-invariant linear sigma model, which is a vector-valued generalization of the Phi(4) quantum field theory, on the three dimensional torus. We study the problem via its stochastic quantization, which yields a coupled system of N interacting SPDEs. We prove tightness of the invariant measures in the large N limit. For large enough mass or small enough coupling constant, they converge to the (massive) Gaussian free field at a rate of order 1/root N with respect to the Wasserstein distance. We also obtain tightness results for certain O( N) invariant observables. These generalize some of the results in Shen et al. (Ann Probab 50(1):131202, 2022) from two dimensions to three dimensions. The proof leverages the method recently developed by Gubinelli and Hofmanova (Commun Math Phys 384(1):1-75, 2021) and combines many newtechniques such as uniform in N estimates on perturbative objects as well as the solutions. |
| 资助项目 | NSF[DMS-1712684 / 1909525] ; NSF[DMS-1954091] ; NSF[CAREER DMS-2044415] ; NSFC[11922103] ; NSFC[12288201] ; NSFC[12090014] ; National Key R&D Program of China[2020YFA0712700] ; key Lab of Random Complex Structures and Data Science, Youth Innovation Promotion Association, Chinese Academy of Science[2020003] ; DFG[CRC 1283] |
| WOS研究方向 | Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000811439200001 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61550]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Shen, Hao |
| 作者单位 | 1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA |
| 推荐引用方式 GB/T 7714 | Shen, Hao,Zhu, Rongchan,Zhu, Xiangchan. Large N Limit of the O(N) Linear Sigma Model in 3D[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2022:57. |
| APA | Shen, Hao,Zhu, Rongchan,&Zhu, Xiangchan.(2022).Large N Limit of the O(N) Linear Sigma Model in 3D.COMMUNICATIONS IN MATHEMATICAL PHYSICS,57. |
| MLA | Shen, Hao,et al."Large N Limit of the O(N) Linear Sigma Model in 3D".COMMUNICATIONS IN MATHEMATICAL PHYSICS (2022):57. |
入库方式： OAI收割
来源：数学与系统科学研究院
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