Berry--Esseen Bounds for High-Temperature Ising Models

@misc{garoni2026berryesseen,
  title = {{Berry--Esseen Bounds for High-Temperature Ising Models}},
  author = {Timothy M. Garoni and Aram Perez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25746},
  eprint = {2610.25746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25746},
}

TY  - UNPB
TI  - Berry--Esseen Bounds for High-Temperature Ising Models
AU  - Timothy M. Garoni
AU  - Aram Perez
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25746
UR  - https://arxiv.org/abs/2610.25746
AB  - We consider the nearest-neighbour Ising model on ℤ^d, and establish sharp results for the normal approximation of the magnetisation throughout the high-temperature regime. In particular, we establish optimal Berry--Esseen bounds between the magnetisation in an arbitrary finite region and a Gaussian with the corresponding finite-volume variance. These results hold for finite-volume Gibbs measures with arbitrary boundary conditions, as well as for the infinite-volume Gibbs measure. We also determine sharp rates of convergence of the magnetisation in a finite box to a Gaussian with variance given by the infinite-volume susceptibility. For this fixed Gaussian target, we show that, in dimensions d≥ 3, periodic boundary conditions yield strictly faster convergence than free boundary conditions. Our approach uses Stein's method to quantify the normal approximation error by analysing the semigroup of the continuous-time Ising heat-bath dynamics.
ER  -