# Bootstrapping the Ising Model on the Lattice

arXiv: https://arxiv.org/abs/2206.12538 · HTML: https://mlsanity.com/paper/2206.12538/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [Convergence of linear programming hierarchies for Gibbs states of spin systems](https://mlsanity.com/paper/2506.06125/) (2025)

## Abstract (arXiv)

We study the statistical Ising model of spins on the infinite lattice using a bootstrap method that combines spin-flip identities with positivity conditions, including reflection positivity and Griffiths inequalities, to derive rigorous two-sided bounds on spin correlators through semi-definite programming. For the 2D Ising model on the square lattice, the bootstrap bounds based on correlators supported in a 13-site diamond-shaped region determine the nearest-spin correlator to within a small window, which for a wide range of coupling and magnetic field is narrower than the precision attainable with Monte Carlo methods. We also report preliminary results of the bootstrap bounds for the 3D Ising model on the cubic lattice.