Percolation of systems having hyperuniformity or giant number fluctuations.

We generate point configurations (PCs) on a square lattice by thresholding the local energy of the Ashkin-Teller model in two dimensions (2D) and study the percolation transition at different values of λ along the critical Baxter line by varying the threshold that controls the particle density ρ. For all values of λ, the PCs exhibit power-law correlations with a decay exponent a that remains independent of ρ and varies continuously with λ. For λ<0, where the PCs are hyperuniform, the percolation critical behavior is identical to that of ordinary percolation. In contrast, for λ>0, the configurations exhibit giant number fluctuations, and all critical exponents vary continuously, but form a superuniversality class of percolation transition in 2D.