Unusual Coulomb phase physics in the arctic square ice

The square ice is a two-dimensional spin liquid hosting a Coulomb phase physics. When constrained under specific boundary conditions, the so-called domain-wall boundary conditions, a phase separation occurs that leads to the formation of a spin liquid confined within a disk surrounded by magnetically ordered regions. Here, we numerically characterize the ground-state properties of this spin liquid, coined the arctic square ice in reference to a phenomenon known in statistical mechanics. Our results reveal that both the vertex distributions and the magnetic correlations are inhomogeneous within the liquid region, and they exhibit a radial dependence. If these properties resemble those of the conventional square ice close to the center of the disk, they evolve continuously as the disk perimeter is approached. There, the spin liquid orders. As a result, pinch points, signaling the presence of algebraic spin correlations, coexist with magnetic Bragg peaks in the magnetic structure factor computed within the disk. The arctic square ice thus appears as an unconventional Coulomb phase sharing common features with a fragmented spin liquid, albeit on a charge-neutral vacuum.