Dynamical transition of glasses: From exact to approximate

被引:50
作者
Mari, Romain [1 ]
Kurchan, Jorge [1 ]
机构
[1] ESPCI ParisTech, CNRS, PMMH, UMR 7636, F-75231 Paris 05, France
关键词
MODE-COUPLING-THEORY; KIRKWOOD-SALSBURG EQUATIONS; MEAN-FIELD THEORY; HARD-SPHERE; STATISTICAL-MECHANICS; THERMODYNAMICS; INSTABILITY; CONNECTIONS; ENERGY; FLUID;
D O I
10.1063/1.3626802
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is exactly described by equations conceptually close, but different from, the mode-coupling equations. We obtain these by a dynamic virial construction. Quite surprisingly, we observe that in three dimensions, the mean-field behavior is closely followed for ranges as small as one interparticle distance, and still qualitatively for smaller distances. For the original particle model, we expect the present mean-field theory to become, unlike the mode-coupling equations, an increasingly good approximation at higher dimensions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3626802]
引用
收藏
页数:21
相关论文
共 66 条
[1]   Algorithmic Barriers from Phase Transitions [J].
Achlioptas, Dimitris ;
Coja-Oghlan, Amin .
PROCEEDINGS OF THE 49TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, 2008, :793-+
[2]  
[Anonymous], 2009, COMPLEX DYNAMICS GLA
[3]   Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics [J].
Berthier, L. ;
Biroli, G. ;
Bouchaud, J.-P. ;
Kob, W. ;
Miyazaki, K. ;
Reichman, D. R. .
JOURNAL OF CHEMICAL PHYSICS, 2007, 126 (18)
[4]   Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations [J].
Berthier, L. ;
Biroli, G. ;
Bouchaud, J.-P. ;
Kob, W. ;
Miyazaki, K. ;
Reichman, D. R. .
JOURNAL OF CHEMICAL PHYSICS, 2007, 126 (18)
[5]   Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition [J].
Biroli, G ;
Bouchaud, JP .
EUROPHYSICS LETTERS, 2004, 67 (01) :21-27
[6]   Lattice glass models -: art. no. 025501 [J].
Biroli, G ;
Mézard, M .
PHYSICAL REVIEW LETTERS, 2002, 88 (02) :4
[7]   Critical fluctuations and breakdown of the Stokes-Einstein relation in the mode-coupling theory of glasses [J].
Biroli, Giulio ;
Bouchaud, Jean-Philippe .
JOURNAL OF PHYSICS-CONDENSED MATTER, 2007, 19 (20)
[8]   Inhomogeneous mode-coupling theory and growing dynamic length in supercooled liquids [J].
Biroli, Giulio ;
Bouchaud, Jean-Philippe ;
Miyazaki, Kunimasa ;
Reichman, David R. .
PHYSICAL REVIEW LETTERS, 2006, 97 (19)
[9]   Mode-coupling approximations, glass theory and disordered systems [J].
Bouchaud, JP ;
Cugliandolo, L ;
Kurchan, J ;
Mezard, M .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 1996, 226 (3-4) :243-273
[10]   Comment on "Probing the Equilibrium Dynamics of Colloidal Hard Spheres above the Mode-Coupling Glass Transition'' Reply [J].
Brambilla, G. ;
El Masri, D. ;
Pierno, M. ;
Berthier, L. ;
Cipelletti, L. .
PHYSICAL REVIEW LETTERS, 2010, 105 (19)