Explain the anomalous local-energy cluster scaling

Determine the origin and asymptotic nature of the apparent power-law cluster-size distribution with exponent \(\tau=1.75\) for clusters of sites whose local energy differs from the ground-state local-energy value in ground-state configurations of the antiferromagnetic Ising model on the Shastry–Sutherland lattice, including whether the scaling persists in the thermodynamic limit or crosses over to exponential decay.

Background

The sampled ground-state configurations contain clusters of sites with local energies different from the mean ground-state local energy. Their observed size distribution is numerically consistent with a power law of exponent $\tau=1.75$, unlike the exponent for ordinary two-dimensional percolation.

The paper does not establish whether this behavior is genuine or a finite-size effect. The authors also state that they are unaware of a related model with the same exponent and cannot explain its origin, leaving the mechanism and asymptotic behavior unresolved.