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

2020/05/19 by Shen, Hao, Smith, Scott, Zhu, Rongchan +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.09279

Abstract

This article studies large N limits of a coupled system of N interacting Φ⁴ equations posed over \mathbbT^d for d=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 invariant measure of the mean-field dynamics, at a rate of order 1/√(N) with respect to the Wasserstein distance. We also consider fluctuations and obtain tightness results for certain O(N) invariant observables, along with an exact description of the limiting correlations.

Cited by

• McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

Related

• Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE
• Hyperbolic O (N) linear sigma model and its mean-field limit
• Large N limit of the Langevin dynamics for the spin O(N) model
• Taming NSPT fluctuations in O(N) Non-Linear Sigma Model: simulations in the large N regime
• NSPT for O(N) non-linear sigma model: the larger N the better