Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calculable baseline for dynamical heterogeneity in glassy systems.
Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
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abstract
We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that relate space and time scales to the distance from criticality, as well as the scaling form of the critical four-point correlation function. However, both these predictions and other well known MCT results are mean-field in nature and are thus expected to change below the upper critical dimension dc=6, as suggested by different forms of the Ginzburg criterion.
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cond-mat.stat-mech 1years
2026 1verdicts
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A Shared Observation Shields Collective Fluctuations while Preserving Local Independence
Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calculable baseline for dynamical heterogeneity in glassy systems.