Connecting real glasses to mean-field models

Abstract

We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo neighbours and by means of analytical calculations, we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with increasing k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the MCT power law behaviour for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with increasing k whereas the non-Gaussian parameter is independent of it. Thus we conclude that with the increase in the number of pseudo neighbours the system becomes more mean-field like. By comparing our results with previous studies on mean-field like system we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit.

19 pages, 21 figures

References in corpus (42)

• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Dynamical heterogeneities in a supercooled Lennard-Jones liquid
• String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility
• The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Fragilities of Liquids Predicted from the Random First Order Transition Theory of Glasses
• Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids
• The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-Order Transition Theories of Glass Formation
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Mode-Coupling Theory of the Glass Transition: A Primer
• How does the relaxation of a supercooled liquid depend on its microscopic dynamics?
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
• Breakdown of the Stokes-Einstein relation in two, three and four dimensions
• Barrier Softening near the onset of Non-Activated Transport in Supercooled Liquids: Implications for Establishing Detailed Connection between Thermodynamic and Kinetic Anomalies in Supercooled Liquids
• Dynamical Exchanges in Facilitated Models of Supercooled liquids
• Correlation of Local Order with Particle Mobility in Supercooled Liquids is Highly System Dependent
• Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
• Finite size effects in the dynamics of glass-forming liquids
• Dimensional Study of the Caging Order Parameter at the Glass Transition
• Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
• Glass transition of hard spheres in high dimensions
• Dynamical transition of glasses: from exact to approximate
• Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities
• On the correlation between fragility and stretching in glassforming liquids
• Dynamic heterogeneities above and below the mode-coupling temperature. Evidence of a dynamic crossover
• Role of saddles in mean-field dynamics above the glass transition
• Dynamic and thermodynamic crossover scenarios in the Kob-Andersen mixture: Insights from multi-CPU and multi-GPU simulations
• Slow Dynamics of the High Density Gaussian Core Model
• Unraveling the success and failure of mode coupling theory from consideration of entropy
• Determination of onset temperature from the entropy for fragile to strong liquids
• Ten themes of viscous liquid dynamics
• Statics and Dynamics of the 10-state mean-field Potts glass model: A Monte Carlo study
• When gel and glass meet: A mechanism for multistep relaxation
• The role of pair correlation function in the dynamical transition predicted by the mode coupling theory
• Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass
• Mean-field dynamic criticality and geometric transition in the Gaussian core model
• Possible Universal Relation Between Short time $\beta$-relaxation and Long time $\alpha$-relaxation in Glass-forming Liquids
• Continuous time random walk concepts applied to extended mode coupling theory: A study of the Stokes-Einstein breakdown
• Analysis of the anomalous mean field like properties of Gaussian core model in terms of entropy

Cited by in corpus (4)

• Creating bulk ultrastable glasses by random particle bonding
• Thermodynamics and its correlation with dynamics in a mean-field model and pinned systems: A comparative study using two different methods of entropy calculation
• Creating equilibrium glassy states via random particle bonding
• Efficient $d$-dimensional molecular dynamics simulations for studies of the glass-jamming transition