DOI: 10.1063/1.2041507. The ideal glass transition of hard spheres

The ideal glass transition of hard spheres

10.1063/1.2041507

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We use the replica method to study the ideal glass transition of a liquid of identical hard spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction φK, in the range of 0.58–0.62, and of the random close packing density φc, in the range of 0.64–0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair-correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at φc is equal to 6. All these results compare well with numerical simulations and with other existing theories.

Bibliography

Parisi, G., & Zamponi, F. (2005). The ideal glass transition of hard spheres. The Journal of Chemical Physics, 123(14).

Authors 2

Giorgio Parisi (first)
Francesco Zamponi (additional)

References 30 Referenced 98

10.1063/1.473004 / J. Chem. Phys. (1996)
10.1063/1.475499 / J. Chem. Phys. (1998)
10.1080/002689798167089 / Mol. Phys. (1998)
10.1209/epl/i2004-10015-y / Europhys. Lett. (2004)
10.1103/PhysRevA.43.5442 / Phys. Rev. A (1991)
10.1103/PhysRevLett.70.2766 / Phys. Rev. Lett. (1993)
10.1126/science.225.4666.978.b / Science (1984)
{'volume-title': 'Metastable liquids', 'year': '1996', 'key': '2023073107592549900_c8'} / Metastable liquids (1996)
10.1063/1.480246 / J. Chem. Phys. (1999)
10.1103/PhysRevLett.83.3214 / Phys. Rev. Lett. (1999)
10.1021/cr60135a002 / Chem. Rev. (Washington, D.C.) (1948)
10.1126/science.267.5206.1924 / Science (1995)
10.1063/1.479193 / J. Chem. Phys. (1999)
10.1088/0305-4470/31/9/001 / J. Phys. A (1998)
10.1063/1.478028 / J. Chem. Phys. (1999)
L. Angelani, G. Foffi, and F. Sciortino, e-print cond-mat/0506447.
10.1103/PhysRevA.27.1053 / Phys. Rev. A (1983)
10.1088/0022-3727/2/6/311 / J. Appl. Phys., J. Phys. D (1969)
10.1098/rspa.1970.0189 / Proc. R. Soc. London, Ser. A (1970)
10.1063/1.1661585 / J. Appl. Phys. (1972)
10.1088/0022-3719/7/15/007 / J. Phys. C (1974)
10.1103/PhysRevB.20.4194 / Phys. Rev. B (1979)
10.1016/S0370-1573(97)00069-0 / Phys. Rep. (1998)
10.1103/PhysRevE.65.031304 / Phys. Rev. E (2002)
{'volume-title': 'Spin Glass Theory and Beyond', 'year': '1987', 'key': '2023073107592549900_c24'} / Spin Glass Theory and Beyond (1987)
10.1103/PhysRevLett.75.2847 / Phys. Rev. Lett. (1995)
10.1103/PhysRevLett.82.747 / Phys. Rev. Lett. (1999)
10.1088/0953-8984/12/29/336 / J. Phys.: Condens. Matter (2000)
{'volume-title': 'Theory of Simple Liquids', 'year': '1986', 'key': '2023073107592549900_c28'} / Theory of Simple Liquids (1986)
10.1088/0953-8984/17/12/L02 / J. Phys.: Condens. Matter (2005)

Dates

Type	When
Created	19 years, 10 months ago (Oct. 5, 2005, 6:38 p.m.)
Deposited	2 years ago (July 31, 2023, 3:59 a.m.)
Indexed	3 weeks ago (Aug. 2, 2025, 1:02 a.m.)
Issued	19 years, 10 months ago (Oct. 7, 2005)
Published	19 years, 10 months ago (Oct. 7, 2005)
Published Online	19 years, 10 months ago (Oct. 7, 2005)
Published Print	19 years, 10 months ago (Oct. 8, 2005)

Funders 0

None

BibTeX

@article{Parisi_2005, title={The ideal glass transition of hard spheres}, volume={123}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.2041507}, DOI={10.1063/1.2041507}, number={14}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Parisi, Giorgio and Zamponi, Francesco}, year={2005}, month=oct }

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