Non-Monotonic Dynamical Correlations Across The Glass Crossover

Corentin C. L. Laudicina; Ilian Pihlajamaa; Liesbeth M. C. Janssen; Thomas Voigtmann; Tommaso Rizzo

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arXiv · 2608.21219

Non-Monotonic Dynamical Correlations Across The Glass Crossover

Corentin C. L. Laudicina·Ilian Pihlajamaa·Liesbeth M. C. Janssen·Thomas Voigtmann·Tommaso Rizzo

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Abstract

The dramatic slowing down of structural relaxation in supercooled liquids is accompanied by the emergence of dynamic heterogeneity. A monotonically increasing dynamical correlation length, measured at the $\alpha$-timescale, is one of the remarkable features of this phenomenon. Here we show that this picture is incomplete: the dynamical correlation length measured in the $\beta$-relaxation regime exhibits a striking non-monotonic temperature dependence, reaching a maximum near the mode-coupling crossover temperature $T_c$ and decreasing upon further cooling, even as local dynamical fluctuations continue to intensify. This behavior suggests a crossover from spatially extended, maximally cooperative motion near $T_c$ to increasingly compact and localized relaxation events below it. We demonstrate that this evolution is quantitatively captured by stochastic beta-relaxation theory, an extension of mode-coupling theory beyond mean-field that explicitly predicts an avoided dynamical transition in finite dimensions. Our results provide the first direct spatial evidence in favor of the avoided-transition picture of the mode-coupling crossover, and establish the peak of the $\beta$-regime correlation length as a robust indicator of the mode-coupling crossover.

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Corentin C. L. Laudicina, Ilian Pihlajamaa, Liesbeth M. C. Janssen, Thomas Voigtmann, Tommaso Rizzo. 2026-08-21. Non-Monotonic Dynamical Correlations Across The Glass Crossover. https://arxiv.org/abs/2608.21219

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