Validity range and merger of distinct aging scales

Characterize the parameter-space limits in which distinct aging scales persist and determine how the single aging scale and common effective temperature are recovered as coupling increases.

Background

The results indicate that sufficiently strong coupling can produce a common effective temperature and a single aging description, whereas weak coupling can preserve two aging scales and distinct effective temperatures. The paper does not determine the full boundary between these regimes or the mechanism by which the two-scale description evolves into the common-m description. This unresolved issue concerns both the dynamical regime diagram and the corresponding hierarchy of static replica solutions.

References

A detailed analysis of the limits of validity of this behaviour in parameter space, and how the single aging scale and effective temperature are recovered, is left for future work.

— Coupling spherical p-spin systems  (2609.17522 - Cipolloni et al., 15 Sep 2026) in Section 6, Conclusions and outlook

Deriving the corresponding local Langevin dynamics would then determine whether these marginal lines indeed mark the onset of dynamical arrest and identify the associated relaxation processes. Furthermore, the aging dynamics of the SK model exhibits an infinite hierarchy of asymptotically separated timescales. Our results raise the interesting question of how this temporal hierarchy relates to the hierarchy of spatial correlation lengths $\xi(q)$.

— Short-Range Vector Spin Glasses: Parisi Hierarchies and Real-Space Ultrametricity  (2610.12441 - Vijay et al., 8 Oct 2026) in Conclusion and outlook, subsection “Spatially resolved dynamics”