Effect of site dilution on the negative-coupling branch of the Ashkin–Teller critical line

Determine whether site dilution alters the clean Ashkin–Teller critical behavior for negative four-spin coupling $J_4<0$, where the clean model has correlation-length exponent $ u>1$, by obtaining more precise estimates of the polarization exponent $[?]$ and correlation-length exponent $ u$.

Background

For the site-diluted square lattice with occupation probability $p=0.75$, the authors find clear evidence that uncorrelated disorder changes the critical behavior on the $J_4>0$ branch, where the clean Ashkin–Teller model has $u[?][?]1$. In contrast, for $J_4<0$, the clean model has $u>1$, so both the Harris and HBV criteria predict irrelevance of disorder. The measured [?] and [?] are broadly compatible with clean behavior, but the measured polarization exponent differs from its clean Coulomb-gas prediction by slightly more than twice the estimated uncertainty. The paper therefore leaves unresolved whether site dilution genuinely changes the critical behavior in this regime.