Glass transition of hard spheres in high dimensions

Details Glass transition of hard spheres in high dimensions Glass transition of hard spheres in high dimensions

2010-03-24

arxiv.org/abs/1003.4559v1

Phys. Rev. E 81, 041502 (2010)

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 8 figures, Phys. Rev. E (in print)

Scientific paper

10.1103/PhysRevE.81.041502

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty $ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d) $ and $f_{c}^{(s)}(k;d) $ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d) $ and $f_{c}(k;d) $ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ 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 $d$.

Affiliated with

Also associated with

No associations

Rating

Glass transition of hard spheres in high dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Glass transition of hard spheres in high dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Glass transition of hard spheres in high dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-56705