• Corpus ID: 218684975

Large $N$ Limit of the $O(N)$ Linear Sigma Model via Stochastic Quantization

@article{Shen2020LargeL,
  title={Large \$N\$ Limit of the \$O(N)\$ Linear Sigma Model via Stochastic Quantization},
  author={Hao Shen and Scott A. Smith and R. Zhu and Xiangchan Zhu},
  journal={arXiv: Probability},
  year={2020}
}
This article studies large $N$ limits of a coupled system of $N$ interacting $\Phi^4$ equations posed over $\mathbb{T}^{d}$ for $d=1,2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well-posed. Moreover, we show tightness of the invariant measures in the large $N$ limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique… 
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References

SHOWING 1-10 OF 78 REFERENCES
Strong solutions to the stochastic quantization equations
We prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure. The method is
1/n expansion for a Quantum Field Model
A nonperturbative study of the 1/n expansion in Euclidean Quantum Field Theory is started. The expansion is shown to be asymptotic to the vacuum energy of the (φ2)22 model, for arbitrary coupling
The strong Feller property for singular stochastic PDEs
We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical $\Phi^4_3$
Quantum field-theory models in less than 4 dimensions
Langevin dynamic for the 2D Yang-Mills measure
We define a natural state space and Markov process associated to the stochastic Yang-Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for
Pathwise McKean–Vlasov theory with additive noise
We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [38]. Our study was prompted by some concrete problems in
Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms
In this paper, we prove the existence of martingale solutions to the stochastic heat equation taking values in a Riemannian manifold, which admits Wiener (Brownian bridge) measure on the Riemannian
The invariant measure and the flow associated to the $\Phi^4_3$-quantum field model
We give a direct construction of invariant measures and global flows for the stochastic quantization equation to the quantum field theoretical $\Phi ^4_3$-model on the $3$-dimensional torus. This
A priori bounds for the $Φ^4$ equation in the full sub-critical regime
We derive a priori bounds for the $\Phi^4$ equation in the full sub-critical regime using Hairer's theory of regularity structures. The equation is formally given by \begin{equation}
Geometric stochastic heat equations
We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorphism group on
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