Finite size scaling analysis of the glass transition

Abstract

We show that finite size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging correlation length at the glass transition whose physical manifestation is the presence of dynamical heterogeneities. We introduce a parameter B(T,L) whose temperature, T, and system size, L, dependences permit a precise location of the glass transition. We discuss the finite size scaling behaviour of a diverging susceptibility χ(L,T). These new techniques are successfully used to study two lattice models. The analysis straightforwardly applies to any glass-forming system.

4 pages, 3 figures

Cited by in corpus (41)

• Theoretical perspective on the glass transition and amorphous materials
• Bond orientational ordering in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization
• Growing length and time scales in glass forming liquids
• What do we learn from the shape of the dynamical susceptibility of glass-formers?
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Time and length scales in supercooled liquids
• Dynamic criticality in glass-forming liquids
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Slow flows of yield stress fluids: complex spatio-temporal behaviour within a simple elasto-plastic model
• Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales
• Spatial structures and dynamics of kinetically constrained models for glasses
• Real space origin of temperature crossovers in supercooled liquids
• Cooperative Strings and Glassy Interfaces
• Finite size effects in the dynamics of glass-forming liquids
• Short-time $\beta$-relaxation in glass-forming liquids is cooperative in nature
• Caging and mosaic lengthscales in plaquette spin models of glasses
• Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres
• Revisiting the slow dynamics of a silica melt using Monte Carlo simulations
• Renormalization group study of a kinetically constrained model for strong glasses
• The Kovacs effect in model glasses
• Fluctuations in glassy systems
• Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
• Slow dynamics of a confined supercooled binary mixture: direct space analysis
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Finite Size Scaling for the Glass Transition: the Role of a Static Length Scale
• Subdiffusion and dynamical heterogeneities in a lattice glass model
• Stress and large-scale spatial structures in dense, driven granular flows
• Lifetime of dynamic heterogeneity in strong and fragile kinetically constrained spin models
• Glassy aspects of melting dynamics (On melting dynamics and the glass transition, Part I)
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Anisotropic spatially heterogeneous dynamics on the $\alpha$ and $\beta$ relaxation time scales studied via a four-point correlation function
• Tracking heterogeneous dynamics during the alpha-relaxation of a simple glass-former
• Spatial correlations in the relaxation of the Kob-Andersen model
• Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry
• Crossover from entropic to thermal dynamics in glassy models
• Slow dynamics of a confined supercooled binary mixture II: Q space analysis
• Dynamic Heterogeneity in the Glauber-Ising chain
• Jamming percolation and glassy dynamics
• Connecting microscopic simulations with kinetically constrained models of glasses
• Inherent structures dynamics in glasses: a comparative study
• Finite-size effects and intermittency in a simple aging system