Dimensional study of the caging order parameter at the glass transition

The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed upon regarding why a fluid becomes sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension d, we find the cage to keep a nontrivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is qualitatively supported here and non-mean-field corrections are found to remain small on decreasing d, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.

[1]  Toy model for the mean-field theory of hard-sphere liquids , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  J. P. Garrahan,et al.  Coarse-grained microscopic model of glass formers , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[3]  T. R. Kirkpatrick,et al.  Scaling concepts for the dynamics of viscous liquids near an ideal glassy state. , 1989, Physical review. A, General physics.

[4]  Ludovic Berthier,et al.  Universal nature of particle displacements close to glass and jamming transitions. , 2007, Physical review letters.

[5]  P. Charbonneau,et al.  Numerical and theoretical study of a monodisperse hard-sphere glass former. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  T. R. Kirkpatrick,et al.  Connections between some kinetic and equilibrium theories of the glass transition. , 1987, Physical review. A, General physics.

[7]  Jean-Philippe Bouchaud,et al.  Critical fluctuations and breakdown of the Stokes–Einstein relation in the mode-coupling theory of glasses , 2006, cond-mat/0609705.

[8]  Andrea Cavagna,et al.  Supercooled liquids for pedestrians , 2009, 0903.4264.

[9]  M. .. Moore,et al.  Renormalization group analysis of the M-p-spin glass model with p=3 and M = 3 , 2011, 1111.3105.

[10]  Giorgio Parisi,et al.  Glass transition and random close packing above three dimensions. , 2011, Physical review letters.

[11]  G. Biroli,et al.  Dynamical Heterogeneities in Glasses, Colloids, and Granular Media , 2011 .

[12]  A. Alexander-Katz,et al.  Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations , 2011, The European physical journal. E, Soft matter.

[13]  Giorgio Parisi,et al.  Quantitative field theory of the glass transition , 2012, Proceedings of the National Academy of Sciences.

[14]  H L Frisch,et al.  High dimensionality as an organizing device for classical fluids. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Kunimasa Miyazaki,et al.  Mode-coupling theory as a mean-field description of the glass transition. , 2010, Physical review letters.

[16]  Peter Harrowell,et al.  How reproducible are dynamic heterogeneities in a supercooled liquid? , 2004, Physical review letters.

[17]  F. Ricci-Tersenghi,et al.  Field theory of fluctuations in glasses , 2011, The European physical journal. E, Soft matter.

[18]  J. P. Garrahan,et al.  Dynamic Order-Disorder in Atomistic Models of Structural Glass Formers , 2009, Science.

[19]  P. Saramito,et al.  Understanding and predicting viscous, elastic, plastic flows , 2011, The European physical journal. E, Soft matter.

[20]  Fast simulation of facilitated spin models , 2005, cond-mat/0510356.

[21]  P. Harrowell,et al.  Non‐Gaussian behavior and the dynamical complexity of particle motion in a dense two‐dimensional liquid , 1996 .

[22]  Thirumalai,et al.  Comparison between dynamical theories and metastable states in regular and glassy mean-field spin models with underlying first-order-like phase transitions. , 1988, Physical review. A, General physics.

[23]  G. Biroli,et al.  Theoretical perspective on the glass transition and amorphous materials , 2010, 1011.2578.

[24]  P. Charbonneau,et al.  Hard-sphere crystallization gets rarer with increasing dimension. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  G. Biroli,et al.  Super-diffusion around the rigidity transition: Levy and the Lilliputians , 2010, 1001.1765.

[26]  Giorgio Parisi,et al.  Glasses and replicas , 2009, 0910.2838.

[27]  Giorgio Parisi,et al.  Mean-field theory of hard sphere glasses and jamming , 2008, 0802.2180.

[28]  Peter G Wolynes,et al.  Theory of structural glasses and supercooled liquids. , 2007, Annual review of physical chemistry.

[29]  G. Biroli,et al.  The Random First-Order Transition Theory of Glasses: a critical assessment , 2009, 0912.2542.

[30]  Steven J. Plimpton,et al.  DYNAMICAL HETEROGENEITIES IN A SUPERCOOLED LENNARD-JONES LIQUID , 1997 .

[31]  Monica L. Skoge,et al.  Packing hyperspheres in high-dimensional Euclidean spaces. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Wolfgang Götze,et al.  Complex Dynamics of Glass-Forming Liquids , 2008 .

[33]  Mode-Coupling as a Landau Theory of the Glass Transition , 2009, 0903.4619.

[34]  Rolf Schilling,et al.  Glass transition of hard spheres in high dimensions. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  J. P. Garrahan,et al.  Excitations Are Localized and Relaxation Is Hierarchical in Glass-Forming Liquids , 2011, 1107.3628.

[36]  Renormalization group analysis of the random first-order transition. , 2010, Physical review letters.