We analyze the ground state properties of the honeycomb Ising antiferromagnet in an external magnetic field. We demonstrate the existence of extensive ground state degeneracy at finite field that maps to a polyhex tiling problem. This state is shown to be a jammed spin liquid, with no local zero modes connecting ground states. Through Monte Carlo simulations, we explore the properties of these states and show that the spin diffusion can be controlled by the magnetic field strength. By considering quantum fluctuations, we demonstrate that transverse coupling partially lifts the ground state degeneracy, selecting an extensive subspace of non-periodic tilings of 12-hexes. We suggest that the jammed polyhex spin liquid phase exists in an experimentally realizable region of parameter space and may be present in the FePX3 compounds.
@article{arxiv.2604.24687,
title = {Field-induced jammed polyhex spin liquid in the honeycomb Ising antiferromagnet},
author = {Nicholas Franklin and Jacob Richards and Harry Lane},
journal= {arXiv preprint arXiv:2604.24687},
year = {2026}
}