Statistical mechanics of coupled supercooled liquids in finite dimensions

Abstract

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon ,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.

arXiv commentMain text of 14 pages, 11 figures + two appendices of 14 pages, 5 figures. Accepted for publication in SciPost Physics

References in corpus (72)

• Theoretical perspective on the glass transition and amorphous materials
• Supercooled Liquids for Pedestrians
• On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses
• The structural glass transition and the entropy of the metastable states
• Spin-Glass Theory for Pedestrians
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• The frustration-based approach of supercooled liquids and the glass transition: a review and critical assessment
• Thermodynamic signature of growing amorphous order in glass-forming liquids
• Models and algorithms for the next generation of glass transition studies
• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Recipes for metastable states in Spin Glasses
• Phase diagram of glassy systems in an external field
• Facets of glass physics
• Equilibrium sampling of hard spheres up to the jamming density and beyond
• The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
• Mermin-Wagner fluctuations in 2D amorphous solids
• Fundamental differences between glassy dynamics in two and three dimensions
• Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling
• Long Wavelength Fluctuations and the Glass Transition in 2D and 3D
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Probing a liquid to glass transition in equilibrium
• Universality in the three-dimensional random-field Ising model
• Perspective: Configurational entropy of glass-forming liquids
• Field Theory of Fluctuations in Glasses
• Zero-temperature glass transition in two dimensions
• Statistical Physics of Structural Glasses
• Constrained Boltzmann-Gibbs measures and effective potential for glasses in hypernetted chain approximation and numerical simulations
• Effective potential in glassy systems: theory and simulations
• Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
• Finite size effects in the dynamics of glass-forming liquids
• Overlap fluctuations in glass-forming liquids
• Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids
• How to compute the thermodynamics of a glass using a cloned liquid
• Glass transition and effective potential in the hypernetted chain approximation
• A phase-separation perspective on dynamic heterogeneities in glass-forming liquids
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Does the Adam-Gibbs relation hold in simulated supercooled liquids?
• A novel approach to numerical measurements of the configurational entropy in supercooled liquids
• Evidence for a disordered critical point in a glass-forming liquid
• Random-field-like criticality in glass-forming liquids
• Point-to-set lengths, local structure, and glassiness
• Dynamic relaxation of a liquid cavity under amorphous boundary conditions
• Susceptibility and Percolation in 2D Random Field Ising Magnets
• Self-induced heterogeneity in deeply supercooled liquids
• Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
• Phase transition for quenched coupled replicas in a plaquette spin model of glasses
• First steps of a nucleation theory in disordered systems
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Liquid-glass transition in equilibrium
• Role of fluctuations in the yielding transition of two-dimensional glasses
• Overlap and activity glass transitions in plaquette spin models with hierarchical dynamics
• Efficient measurement of point-to-set correlations and overlap fluctuations in glass-forming liquids
• Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions
• Universality Classes of Critical Points in Constrained Glasses
• Configurational entropy of polydisperse supercooled liquids
• Normal form for renormalization groups
• Replica theory for fluctuations of the activation barriers in glassy systems
• Transition in coupled replicas may not imply a finite temperature ideal glass transition in glass forming systems
• Tethered Monte Carlo: computing the effective potential without critical slowing down
• Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models
• Random-field Ising model criticality in a glass-forming liquid
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Colloid-polymer mixtures in random porous media: Finite size scaling and connected versus disconnected susceptibilities
• Critical scaling in random-field systems: 2 or 3 independent exponents?
• Activated dynamic scaling in the random-field Ising model: a nonperturbative functional renormalization group approach
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
• Role of fluctuations in the phase transitions of coupled plaquette spin models of glasses
• On the overlap between configurations in glassy liquids
• Tethered Monte Carlo: Managing rugged free-energy landscapes with a Helmholtz-potential formalism
• Large deviations of glassy effective potentials
• Structure and dynamics of coupled viscous liquids
• First Principle Computation of Random Pinning Glass Transition, Glass Cooperative Length-Scales and Numerical Comparisons

Cited by in corpus (14)

• Thirty milliseconds in the life of a supercooled liquid
• Modern computational studies of the glass transition
• Computer simulations of the glass transition and glassy materials
• Monte Carlo simulations of glass-forming liquids beyond Metropolis
• Collective relaxation dynamics in a three-dimensional lattice glass model
• Kauzmann Paradox: a crossover due to diminishing local excitations
• Selecting Relevant Structural Features for Glassy Dynamics by Information Imbalance
• Characterising the slow dynamics of the swap Monte Carlo algorithm
• Heterogeneous nucleation in the random field Ising model
• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Pole Analysis of the Inter-Replica Correlation Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the Cluster Glass Phase
• Dynamical Cavity Method for Hypergraphs and its Application to Quenches in the k-XOR-SAT Problem
• Rényi complexity in mean-field disordered systems
• Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope