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Updated: Jun 12, 2026

Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films
Published on: January 26, 2016
Glass transition of hard spheres in high dimensions
Bernhard Schmid1, Rolf Schilling
1Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany.
Abstract:
We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d-->infinity in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters fc(k;d) and fc(s)(k;d) exhibit non-Gaussian k dependence even up to d=800.fc(s)(k;d) and fc(k;d) differ for k approximately d1/2, but become identical on a scale k approximately d, which is proven analytically. The critical packing fraction phic(d) approximately d(2)2(-d) is above the corresponding Kauzmann packing fraction phiK(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d, even for the largest values of d.
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