Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel

Abstract

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter $\sigma$ confined to a two-dimensional channel of width $1.95\sigma$ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ${\varphi }_K$ that is less than the maximum possible ${\varphi }_{\max }$, the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any \emph{real} divergence of the pressure at ${\varphi }_K$. We give arguments that this avoided phase transition is a structural feature -- the remnant in our narrow channel system of the hexatic to crystal transition -- but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ${\tilde{\xi }}_3$ as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around $15\sigma$ at ${\varphi }_K$, which is larger than the penetration lengths that have been reported for three dimensional systems. It is argued that the $\alpha$-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ${\varphi }_K$.

arXiv comment17 pages, 16 figures

References in corpus (28)

• Mean field theory of hard sphere glasses and jamming
• Two-step melting in two dimensions: First-order liquid-hexatic transition
• The role of local structure in dynamical arrest
• The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
• Why is Random Close Packing Reproducible?
• Static point-to-set correlations in glass-forming liquids
• Nonequilibrium glassy dynamics of self-propelled hard disks
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• A first-order phase transition at the random close packing of hard spheres
• Order in glassy systems
• Strong geometric frustration in model glassformers
• Numerical determination of the exponents controlling the relationship between time, length and temperature in glass-forming liquids
• Simulation-based equation of state of the hard disk fluid and prediction of higher-order virial coefficients
• Dynamic relaxation of a liquid cavity under amorphous boundary conditions
• The Complete Jamming Landscape of Confined Hard Discs
• Renormalization group analysis of the random first order transition
• Static and dynamical properties of a hard-disk fluid confined to a narrow channel
• Structural properties of hard disks in a narrow tube
• The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram
• Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
• Renormalization group analysis of the M-p-spin glass model with p=3 and M=3
• Hard Disks in Narrow Channels
• Surface tension fluctuations and a new spinodal point in glass-forming liquids
• Free volume distribution of nearly jammed hard sphere packings
• Static correlations functions and domain walls in glass-forming liquids: the case of a sandwich geometry
• Interface free energies in p-spin glass models
• Transition state theory and the dynamics of hard disks
• Estimation of critical exponents from the cluster coefficients: Application to hard spheres

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• The Gardner transition in physical dimensions
• Assembly of hard spheres in a cylinder: a computational and experimental study
• Glass-like behavior of a hard-disk fluid confined to a narrow channel
• Correlation lengths in quasi-one-dimensional systems via transfer matrices
• Marginally jammed states of hard disks in a one-dimensional channel
• Ordering of hard rectangles in strong confinement
• Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]
• Equation of state of hard-disk fluids under single-file confinement
• Clustering and assembly dynamics of a one-dimensional microphase former
• Structural properties of hard-disk fluids under single-file confinement
• Analytical canonical partition function of a quasi-one dimensional system of hard disks
• Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares
• Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement
• Inherent Structure Landscape of Hard Spheres Confined to Narrow Cylindrical Channels
• Density scaling of generalized Lennard-Jones fluids in different dimensions
• Phase behaviour and correlations of parallel hard squares: From highly confined to bulk systems
• Critical behavior of hard squares in strong confinement
• Universality of the close packing properties and markers of isotropic-to-tetratic crossover in quasi-one-dimensional superdisk fluid
• Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks
• Ordering properties of anisotropic hard bodies in one-dimensional channels
• Resolving the two-dimensional ANNNI model using transfer matrices
• Visualizing Free Energy Landscapes for Four Hard Disks
• Competition between shape anisotropy and deformation in the ordering and close packing properties of quasi-one-dimensional hard superellipse fluids
• Positional ordering of hard adsorbate particles in tubular nanopores
• Ordering and association of patchy particles in quasi-one-dimensional channel
• The Gardner correlation length scale in glasses
• Highly confined mixtures of parallel hard squares: A Density Functional Theory study
• Hard disks confined within a narrow channel
• Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices