Large $N$ limit of the $O(N)$ linear sigma model in 3D
Autor: | Hao Shen, Rongchan Zhu, Xiangchan Zhu |
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Rok vydání: | 2021 |
Předmět: | |
DOI: | 10.48550/arxiv.2102.02628 |
Popis: | 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 $1/\sqrt N$ with respect to the Wasserstein distance. We also obtain tightness results for certain $O(N)$ invariant observables. These generalize some of the results in \cite{SSZZ20} from two dimensions to three dimensions. The proof leverages the method recently developed by \cite{GH18} and combines many new techniques such as uniform in $N$ estimates on perturbative objects as well as the solutions. Comment: 46 pages |
Databáze: | OpenAIRE |
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