Determine whether slowly decaying corrections affect the J–Q2 stiffness scaling

Determine whether very slowly decaying finite-size corrections affect the apparent logarithmic growth of Lρ_s(L) at the J–Q2 transition, despite the vanishing bulk stiffness.

Background

The supplemental material discusses competing interpretations of the stiffness behavior in the uniform J–Q2 antiferromagnet at its estimated transition. Earlier work found increasing Lρ_s(L) consistent with logarithmic growth, while another proposal described the behavior using a power law with corrections and two correlation-length exponents. The presence of very slowly decaying corrections would affect the interpretation of finite-size stiffness data and the inferred approach to the thermodynamic limit.

The issue remains unresolved because the available finite-size trends can accommodate more than one continuous-transition description, and the later extrapolation to a nonzero limiting stiffness is explicitly characterized as an unresolved extrapolation rather than a resolved plateau.

References

For J--Q_2 at the estimated transition, Sandvik instead found increasing $L\rho_s(L)$ consistent with $\ln(L/L_0)$, where $L_0$ is a microscopic length; very slowly decaying corrections could not be excluded.

— Collective Symmetry and Criticality from Single-Component Fluctuations  (2609.19629 - Guo et al., 17 Sep 2026) in Section 2.3, subsection “Dimensionless stiffness and the fixed-amplitude limit”