6533b7cffe1ef96bd1259a35

RESEARCH PRODUCT

Glass transition of hard spheres in high dimensions

B. SchmidRolf Schilling

subject

Condensed matter physicsStatistical Mechanics (cond-mat.stat-mech)FOS: Physical sciencesGeometryScale (descriptive set theory)Hard spheresCondensed Matter - Soft Condensed MatterAtomic packing factorQuadratic equationExponentSoft Condensed Matter (cond-mat.soft)Glass transitionCritical exponentCondensed Matter - Statistical MechanicsMathematics

description

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 $d$.

https://dx.doi.org/10.48550/arxiv.1003.4559