Establish whether logarithmic corrections occur at the crossover

Determine whether logarithmic corrections to scaling occur at the crossover point alpha_star = 11/4, where the nonanalytic long-range contribution to the Euler field and the regular linear contribution have the same momentum power.

Background

Within the Gaussian asymptotic closure, the crossover occurs at alpha_star = 11/4. At this value, the two competing contributions to the small-momentum Euler field have coincident powers. Coincident asymptotic powers commonly permit logarithmic modifications, but the paper does not determine whether such terms are actually present in this model.

References

At this point the two powers coincide and logarithmic corrections are not excluded.

— Universal Quantum Criticality from a Gaussian Variational Manifold  (2610.26246 - Khasseh et al., 19 Oct 2026) in Main text, paragraph following Eq. (xsigma-main); End Matter, paragraph following Eq. (sm-phase-closure)