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arXiv · 2511.06196

Central limit theorem for high temperature spin models via martingale embedding

Xiao Fang·Yang Xie·Yi-Kun Zhao
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Abstract

We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving two-point and three-point functions for the CLT in 2-Wasserstein distance. We present three illustrative applications: Ising model with finite-range interactions, ferromagnetic Ising model under the Dobrushin condition, and the Sherrington-Kirkpatrick spin glass model at sufficiently high temperature. In all the examples, we allow heterogeneous external fields.

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Xiao Fang, Yang Xie, Yi-Kun Zhao. 2025-11-09. Central limit theorem for high temperature spin models via martingale embedding. https://arxiv.org/abs/2511.06196

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