---
_id: '64816'
abstract:
- lang: eng
  text: "We study a block mean-field Ising model with $N$ spins split into $s_N$ blocks,
    with Curie-Weiss interaction within blocks and nearest-neighbor coupling between
    blocks. While previous models deal with the block magnetization for a fixed number
    of blocks, we study the the simultaneous limit $N\\to\\infty$ and $s_N\\to\\infty$.
    The model interpolates between Curie-Weiss model for $s_N=1$, multi-species mean
    field for fixed $s_N=s$, and the 1D Ising model for each spin in its own block
    at $s_N=N$.\r\n  Under mild growth conditions on $s_N$, we prove a law of large
    numbers and a multivariate CLT with covariance given by the lattice Green's function.
    For instance, the high temperature CLT essentially covers the optimal range up
    to $s_N=o(N/(\\log N)^c)$ and the low temperature regime is new even for fixed
    number of blocks $s > 2$. In addition to the standard competition between entropy
    and energy, a new obstacle in the proofs is a curse of dimensionality as $s_N
    \\to \\infty$."
author:
- first_name: Jonas
  full_name: Jalowy, Jonas
  id: '113768'
  last_name: Jalowy
  orcid: 0000-0001-9624-2685
- first_name: Isabel
  full_name: Lammers, Isabel
  last_name: Lammers
- first_name: Matthias
  full_name: Löwe, Matthias
  last_name: Löwe
citation:
  ama: Jalowy J, Lammers I, Löwe M. The infinite block spin Ising model. <i>arXiv:260301994</i>.
    Published online 2026.
  apa: Jalowy, J., Lammers, I., &#38; Löwe, M. (2026). The infinite block spin Ising
    model. In <i>arXiv:2603.01994</i>.
  bibtex: '@article{Jalowy_Lammers_Löwe_2026, title={The infinite block spin Ising
    model}, journal={arXiv:2603.01994}, author={Jalowy, Jonas and Lammers, Isabel
    and Löwe, Matthias}, year={2026} }'
  chicago: Jalowy, Jonas, Isabel Lammers, and Matthias Löwe. “The Infinite Block Spin
    Ising Model.” <i>ArXiv:2603.01994</i>, 2026.
  ieee: J. Jalowy, I. Lammers, and M. Löwe, “The infinite block spin Ising model,”
    <i>arXiv:2603.01994</i>. 2026.
  mla: Jalowy, Jonas, et al. “The Infinite Block Spin Ising Model.” <i>ArXiv:2603.01994</i>,
    2026.
  short: J. Jalowy, I. Lammers, M. Löwe, ArXiv:2603.01994 (2026).
date_created: 2026-03-03T08:49:16Z
date_updated: 2026-03-03T08:49:33Z
department:
- _id: '94'
external_id:
  arxiv:
  - '2603.01994'
language:
- iso: eng
publication: arXiv:2603.01994
status: public
title: The infinite block spin Ising model
type: preprint
user_id: '113768'
year: '2026'
...