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.
Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
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abstract
Mode-coupling theory (MCT) is conjectured to be a mean-field description of dynamics of the structural glass transition and the replica theory to be its thermodynamic counterpart. However, the relationship between the two theories remains controversial and quantitative comparison is lacking. In this Letter, we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions above three and compare the results with replica theory. We find grave discrepancies between the predictions of two theories. While MCT describes the nonergodic parameter quantitatively better than the replica theory in three dimension, it predicts a completely different dimension dependence of the dynamical transition point. We find it to be due to the pathological behavior of the nonergodic parameters derived from MCT, which exhibit negative tails in real space at high dimensions.
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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.