Synchronization critical dynamics in higher spatial dimensions

Investigate the nonequilibrium critical dynamics of synchronization in oscillator lattices for spatial dimensions d>1, determining the emergent universality classes, scaling exponents, and fluctuation statistics, and whether the KPZ/EW phenomenology and crossovers found in one dimension persist in higher dimensions.

Background

The present work establishes one-dimensional universal behavior and crossovers linking synchronization dynamics to KPZ/EW universality classes under different types of randomness.

The authors explicitly note that higher-dimensional cases have not yet been studied and point to phenomenological similarities and prior indications suggesting that a similar program might be feasible, highlighting the open direction to extend and test the framework in d>1.

References

While the case of higher dimensions has not yet been studied, as far as we know, there are some indications showing that a similar analysis might be performed ; see also the phenomenological similarities between the profiles arising from the columnar KPZ equation in two dimensions and the phase interfaces displayed in Ref..

— Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices  (2501.11432 - Gutierrez et al., 20 Jan 2025) in Discussion and Conclusions

It remains to analyze the neighborhood of the critical point controlled by EW-type surface fluctuations, as well as other trajectories that approach criticality governed by KPZ-type behavior.

— Critical behavior and crossover scaling in the Light-Heavy model  (2608.18016 - Prakash et al., 18 Aug 2026) in Section 4, “FDPO-like behavior in the disordered phase”