Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 25: Glasses II (joint session of CPP, DF, DY)
DY 25.5: Talk
Thursday, March 25, 2010, 10:45–11:00, H38
Glass transition in high dimensions — •Bernhard Schmid and Rolf Schilling — Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
We have studied the glass transition of hard spheres with diameter σ for dimensions d→ ∞ in the framework of mode-coupling theory (MCT). Assuming that the direct correlation function equals the Mayer function in the limit of high dimensions, we have solved numerically the MCT equations [1] up to d=800. The numerical results for the critical collective and self nonergodicity parameters fc( k;d) and fc( s) ( k;d) exhibit no Gaussian k-dependence even for d=800. Instead they can be represented by a master function, which vanishes for kσ >k0d3/2 with k0≅ 0.15. Inspired by these results, we were able to prove analytically that fc( k;d) converges to fc( s) ( k;d) for kσ =O( d) and d→ ∞ and that the critical packing fraction is given by ϕ c( d) ∼ d22−d. The non-Gaussian character of fc( k;d) and fc( s) ( k;d) implies that the hard sphere glass at ϕ c( d) is not a harmonic solid, even in the limit of high dimensions.
[1] M. Bayer, J.M. Brader, F. Ebert, M. Fuchs, E. Lange, G. Maret, R. Schilling, M. Sperl and J.P. Wittmer, Phys. Rev. E 76, 011508 (2007)