Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition

By Giulio Biroli, Jean-Philippe Bouchaud. 2004

135 citations recorded by the source corpus.

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 ν 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.

Subfields: Ceramics and Composites, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/dd1b40718fd4fe4f55c1460d89e0f7ef162e6c63

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In Ceramics and Composites

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Theoretical perspective on the glass transition and amorphous materials (2010, methodology): “The first full MCT analysis was developed in (Biroli and Bouchaud, 2004), using a field-theoretical approach.”
Mode-coupling theory (2005, background): “Recent work by Biroli and Bouchaud [ 19 ], motivated by the earlier insight of Franz and Parisi [20] and Kirkpatrick and Thirumalai [21], shows that MCT may make quantitative statements about the scales of length and time associated with dynamical heterogeneity.”
Nonequilibrium fluctuations in small systems: From physics to biology (2007, background): “Susceptibilities in glasses are usually defined in terms of four-point correlation functions (two-point in space and two-point in time) which give information about how spatially separated regions are correlated in time [146].”
Slow dynamics in glassy soft matter (2005, background): “However, we note that recent numerical and theoretical work has shown that the concept of the glass transition being a dynamical critical phenomenon can also be successfully applied to Lennard-Jones glass formers [136] and in the framework of the mode coupling theory [139].”
The shapes of cooperatively rearranging regions in glass-forming liquids (2005, background): “According to our theory, the dynamical crossover from activated motion has a spinodal characte”
Mode-Coupling Theory of the Glass Transition: A Primer (2018, background): ““Inhomogeneous” Mode-Coupling Theory: A Measure for Dynamic Heterogeneity As noted earlier, standard MCT seeks to describe the “average” F(k, t) for a given set of wavevectors and system parameters, but does not give immediate access to the fluctuations of F(k, t) that are encoded in the dynamic sus”