Hyperuniformity in Ashkin-Teller model.

We show that equilibrium systems in d dimension that obey the inequalitydν>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 ν varies continuously with the inter-spin interaction strength λ and exceeds the valued2set by Harris criterion when λ is negative; there, the variance of the subsystem energy across a length scale l varies asld-αwith hyperuniformity exponentα=2(1-ν-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 exponentα.