Determine thermodynamic-limit magnetization of the J1-J2 Heisenberg model

Determine whether the antiferromagnetic spin-1/2 J1-J2 Heisenberg model on the square lattice has nonzero site magnetization in the thermodynamic limit as a function of the coupling ratio J2/J1.

Background

The paper notes that every finite spin lattice has zero ground-state magnetization, regardless of the ratio J2/J1. It then identifies an unresolved issue for the infinite square-lattice system: whether spontaneous magnetization can persist in the thermodynamic limit. The authors estimate magnetization using a small symmetry-preserving magnetic-field perturbation and finite differences, but their finite-order perturbative and coupled-cluster calculations do not settle the underlying thermodynamic-limit question.

References

There are still debates as to whether there is any magnetization in the TDL.

— Examining Convergence of Cluster Perturbation Theory and Cluster Coupled Cluster for J1-J2 Heisenberg Spin Lattices  (2609.08768 - Keyes et al., 8 Sep 2026) in Section 2, subsection “Magnetization”