The Rate of Convergence of the Critical Mean-Field O(N) Magnetization Via Multivariate Nonnormal Stein’s Method
Abstract
Abstract We study the distribution of the magnetization of the critical mean-field O ( N ) model with $$N\ge 2$$ N ≥ 2 . Specifically, we bound the Wasserstein distance between the finite-volume and limiting distributions, in terms of the number of spins. To achieve this, we extend a recent multivariate nonnormal approximation theorem. This generalizes known results for the Curie-Weiss magnetization to the multivariate O ( N ) setting.
Fields of Study & Subjects
Random Matrices and Applications
Theoretical and Computational Physics
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Journal of Statistical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 193
- Issue
- 6
- Publication date
- 26 May 2026
- Language
- EN