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Large N Limit of the O(N) Linear Sigma Model in 3D
Shen, Hao1; Zhu, Rongchan2; Zhu, Xiangchan3
AbstractIn 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.
Indexed BySCI
Funding ProjectNSF[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 AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000811439200001
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Document Type期刊论文
Corresponding AuthorShen, Hao
Affiliation1.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
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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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