Clarify the origin of tail saturation in two-dimensional four-point correlations

Determine the precise origin of the saturation of the large-distance tail of the four-point correlation function in the two-dimensional model glass former, including whether it is caused by Mermin–Wagner fluctuations.

Background

The supplementary analysis reports that the two-dimensional four-point correlation function sometimes develops a saturated rather than cleanly exponential tail. The authors suggest that Mermin–Wagner fluctuations may cause this behavior, while noting that bond-breaking mobility indicators suppress the effect and restore the expected negative tails. The precise mechanism is therefore not established.

References

Interestingly, in two dimensions $G_4(r,t)$ sometimes tends to exhibit a saturation of the tail rather than a clean exponential decay. Although the precise origin of this behaviour is not fully understood, it is likely linked to the presence of Mermin–Wagner (MW) fluctuations in the two-dimensional system .

— Non-Monotonic Dynamical Correlations Across The Glass Crossover  (2608.21219 - Laudicina et al., 21 Aug 2026) in Supplementary Information, Section 2, subsection “Fluctuations of the Self-Overlap Function”