Hyperuniformity in Ashkin-Teller model

We show that equilibrium systems in $d$ dimension that obey the inequality $d\nu> 2,$ known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example in $d=2$ where the correlation length exponent $\nu$ varies continuously with the inter-spin interaction strength $\lambda$ and exceeds the value $\frac d2$ set by Harris criterion when $\lambda$ is negative; there, the variance of the subsystem energy across a length scale $l$ varies as $l^{d-\alpha}$ with hyperuniformity exponent $\alpha = 2(1-\nu^{-1}).$ Point configurations constructed by assigning unity to the sites which has coarse-grained energy beyond a threshold value also exhibit suppressed number fluctuation and hyperuniformiyty with same exponent $\alpha.$