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<p>We study the distribution of the magnetization of the critical mean-field <i>O</i>(<i>N</i>) model with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. 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 <i>O</i>(<i>N</i>) setting.</p>

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The Rate of Convergence of the Critical Mean-Field O(N) Magnetization Via Multivariate Nonnormal Stein’s Method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Timothy M. Garoni,
  • Aram Perez,
  • Zongzheng Zhou

摘要

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.