Hyperuniformity in Ashkin-Teller model

TL;DR

This paper demonstrates that the Ashkin-Teller model in two dimensions exhibits hyperuniform energy fluctuations at criticality when the correlation length exponent exceeds a certain threshold, revealing suppressed fluctuations and hyperuniformity.

Contribution

It shows that the Ashkin-Teller model exhibits hyperuniformity in energy fluctuations at criticality, especially when the correlation length exponent exceeds the Harris criterion threshold.

Findings

Energy variance scales as l^{d - alpha} with alpha = 2(1 - 1/nu).

Point configurations based on energy thresholds also show hyperuniformity.

The hyperuniformity exponent relates directly to the correlation length exponent nu.

Abstract

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 $\alpha.$