Characterize the maximally degenerate ground state at the transition coupling

Characterize the nature of the zero-temperature ground state of the classical antiferromagnetic Ising model on the Shastry–Sutherland lattice at the limiting interaction strength \(\alpha=1\), where the Néel and dimer states have equal energy and the ground state is macroscopically degenerate.

Background

For diagonal coupling ratio $\alpha<1$, the model has an antiferromagnetically ordered Néel ground state, whereas for $\alpha>1$ it has a macroscopically degenerate antiferromagnetic dimer ground state. At $\alpha=1$, these two classes of configurations have identical energy, producing an even larger and more complicated ground-state degeneracy.

The paper estimates the residual entropy and examines sampled ground-state configurations, correlations, and local-energy clusters, but does not provide a complete characterization of the ground-state manifold. The authors explicitly identify the nature of this state as not fully understood.