Hyperuniformity in Ashkin-Teller model

Abstract

We show that equilibrium systems in $d$ dimension that obey the inequality $d\hat{I}½>2,$ 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 $\hat{I}½$ varies continuously with the inter-spin interaction strength $\hat{I}»$ and exceeds the value $\frac{d}{2}$ set by Harris criterion when $\hat{I}»$ is negative; there, the variance of the subsystem energy across a length scale $l$ varies as $l^{d-\hat{I}\pm }$ with hyperuniformity exponent $\hat{I}\pm =2(1-\hat{I}{½}^{-1}).$ 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 $\hat{I}\pm .$

13 pages, 5 figs