Determine the nonlinear strong-coupling behavior of two-dimensional gradient activity

Determine the genuinely nonlinear functional-renormalization-group behavior of gradient activity in two dimensions, where gradient activity is canonically marginal, and characterize the associated strong-coupling regime and logarithmic signatures.

Background

The analysis is restricted to the three-dimensional critical basin of the passive conserved Wilson–Fisher fixed point. The authors note that in two dimensions gradient activity becomes canonically marginal, so the linearized three-dimensional spectrum does not settle its infrared behavior.

A genuinely nonlinear functional RG treatment is therefore needed to determine whether the marginal activity remains marginal, becomes marginally relevant or irrelevant, or flows into a strong-coupling regime, and to characterize the logarithmic behavior sought in deterministic Active Model B and Active Model B+ simulations.

References

In two dimensions gradient activity is canonically marginal, a prediction whose logarithmic signature has recently been looked for in deterministic simulations of Active Model B and B+, and requires a genuinely nonlinear functional RG treatment; we leave that distinct strong-coupling problem for separate work.

— Nonequilibrium corrections to conserved Ising criticality in scalar active matter: Ward identities, spectrum, and long crossovers  (2609.02351 - Zdybel, 2 Sep 2026) in Section 6, “Discussion and conclusions”