KMS Of Academy of mathematics and systems sciences, CAS
Large N Limit of the O(N) Linear Sigma Model in 3D | |
Shen, Hao1; Zhu, Rongchan2; Zhu, Xiangchan3 | |
2022-06-16 | |
Source Publication | COMMUNICATIONS IN MATHEMATICAL PHYSICS |
ISSN | 0010-3616 |
Pages | 57 |
Abstract | 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. |
DOI | 10.1007/s00220-022-04414-w |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Physics |
WOS Subject | Physics, Mathematical |
WOS ID | WOS:000811439200001 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/61551 |
Collection | 应用数学研究所 |
Corresponding Author | Shen, Hao |
Affiliation | 1.Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA 2.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
Recommended Citation 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. |
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