Fig. 4

Numerical results. Snapshots of numerical simulations for increasing decimation with color coding as in Fig. 2(b) indicating vertex charges. At zero decimation (η = 0) large regions of the expected antiferromagnetic order separated by domain walls are visible. At low decimation of 2–6% (η = 0.086,η = 0.315), almost all of the z = 3 vertices are positively charged, while negative charges (q = −2) that appear on the z = 4 vertices can pin the domain walls, causing the ordered domains to shrink. At a decimation of 12%, there is already no discernible order, while at high decimation, about half of the z = 4 vertices violate the ice rule and host positive charges, which destroy the remaining ordering. In the zoomed portion of the ξ = 12% and η = 0.923 sample, the colloidal positions are visible and show details of violation of the ice rule at z = 4 vertices by negative, q = −2 monopoles only, but little or no ice rule violation at z = 3 vertices. See Supplementary Movies 3–6 for corresponding movie clips