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arXiv · 2410.19425

Lattice study of RG fixed point based on gradient flow in $3$D $O(N)$ sigma model

Okuto Morikawa·Mizuki Tanaka·Masakiyo Kitazawa·Hiroshi Suzuki
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Abstract

We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis based on the gradient flow in the large $N$ approximation at criticality. Then, we work out the numerical simulation of the theory with finite $N$. Depicting the renormalization group flow along the gradient flow, we confirm the existence of the Wilson--Fisher fixed point non-perturbatively.

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Okuto Morikawa, Mizuki Tanaka, Masakiyo Kitazawa, Hiroshi Suzuki. 2024-10-25. Lattice study of RG fixed point based on gradient flow in $3$D $O(N)$ sigma model. https://arxiv.org/abs/2410.19425

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