Field Theory of Fluctuations in Glasses

Abstract

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be describes through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.

References in corpus (41)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Direct experimental evidence of a growing length scale accompanying the glass transition
• Irreversible reorganization in a supercooled liquid originates from localised soft modes
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• The structural glass transition and the entropy of the metastable states
• Exact Renormalization Group Equations. An Introductory Review
• Mode-Coupling Theory (MCT) Lecture Notes
• Predicting the long time dynamic heterogeneity in a supercooled liquid on the basis of short time heterogeneities
• Recipes for metastable states in Spin Glasses
• Growing length and time scales in glass forming liquids
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Phase diagram of glassy systems in an external field
• On nonlinear susceptibility in supercooled liquids
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• Structure and dynamics in glass-formers: predictability at large length scales
• Self Induced Quenched Disorder: A Model for the Glass Transition
• On the Study of Collective Dynamics in Supercooled Liquids through the Statistics of the Iso-Configurational Ensemble
• On the dynamics of the glass transition on Bethe lattices
• Effective potential in glassy systems: theory and simulations
• On the cooling-schedule dependence of the dynamics of mean-field glasses
• Spatially heterogeneous ages in glassy dynamics
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
• Separation of time-scales and reparametrization invariance for aging systems
• On the relationship between structure and dynamics in a supercooled liquid
• Mode-Coupling as a Landau Theory of the Glass Transition
• Fluctuations in glassy systems
• Kob-Andersen model: a non-standard mechanism for the glassy transition
• Generic replica symmetric field-theory for short range Ising spin glasses
• Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
• Glassy dynamics as a melting process (On melting dynamics and the glass transition, Part II)
• The Random First-Order Transition Theory of Glasses: a critical assessment
• On the probabilistic formulation of the replica approach to spin glasses
• 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
• Finite dimensional corrections to mean field in a short-range p-spin glassy model
• Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables
• Properties of the perturbative expansion around the mode-coupling dynamical transition in glasses
• Replica Field Theory of the Dynamical Transition in Glassy Systems
• Critical behaviour of large scale dynamical heterogeneities in glasses: a complete theory

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• Perspective: The Glass Transition
• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• Solution of the dynamics of liquids in the large-dimensional limit
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• Correlation of Local Order with Particle Mobility in Supercooled Liquids is Highly System Dependent
• Finite size effects in the dynamics of glass-forming liquids
• Shear yielding and shear jamming of dense hard sphere glasses
• Dimensional Study of the Caging Order Parameter at the Glass Transition
• Quantitative field theory of the glass transition
• On the critical slowing down exponents of mode coupling theory
• Random-field-like criticality in glass-forming liquids
• Critical Dynamics in Glassy Systems
• Deconstructing the glass transition through critical experiments on colloids
• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Dimensional dependence of the Stokes--Einstein relation and its violation
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics
• Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function
• Liu-Nagel phase diagrams in infinite dimension
• Phase transition for quenched coupled replicas in a plaquette spin model of glasses
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Quantitative approximation schemes for glasses
• Universality Classes of Critical Points in Constrained Glasses
• Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids
• Static replica approach to critical correlations in glassy systems
• Long-wavelength fluctuations lead to a model of the glass crossover
• Dynamical Landau Theory of the Glass Crossover
• Polymer Glass-Formation in Variable Dimension
• Universal non-mean-field scaling in the density of state of amorphous solids
• Finite-dimensional vestige of spinodal criticality above the dynamical glass transition
• On the two-steps relaxation of mean-field glasses: p-spin model
• Yielding and plasticity in amorphous solids
• Solvable Models of Supercooled Liquids in Three Dimensions
• Local dynamical heterogeneity in glass formers
• Statistical mechanics of coupled supercooled liquids in finite dimensions
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Glassy Critical Points and Random Field Ising Model
• Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition
• Quasi-equilibrium in glassy dynamics: an algebraic view
• Scaling and universality in glass transition
• Critical dynamical heterogeneities close to continuous second-order glass transitions
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
• Fluctuations and Shape of Cooperative Rearranging Regions in Glass-Forming Liquids
• Microscopic models of mode-coupling theory: the $F_{12}$ scenario
• Equilibrium Fluctuations in Mean-field Disordered Models
• On the overlap between configurations in glassy liquids
• Quasi-equilibrium in glassy dynamics: a liquid theory approach
• Mean-field description for the architecture of low-energy excitations in glasses
• Different glassy characteristics are related to either caging or dynamical heterogeneity
• On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory
• Finite-size critical fluctuations in microscopic models of mode-coupling theory
• The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions
• Large deviations of glassy effective potentials
• Thermal vestiges of avalanches in the driven random field Ising model
• Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach
• Dynamic Length Scales in Glass-Forming Liquids: A Inhomogeneous Molecular Dynamics Simulation Approach
• Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models
• Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables
• The Glass Crossover from Mean-Field Spin-Glasses to Supercooled Liquids
• Fluctuations in the Time Variable and Dynamical Heterogeneity in Glass-Forming Systems
• Inverse problem for multi-body interaction of nonlinear waves
• Precursors of the Spin Glass Transition in Three Dimensions
• First Principle Computation of Random Pinning Glass Transition, Glass Cooperative Length-Scales and Numerical Comparisons
• Dynamics and fluctuations of minimally-structured glass formers
• Fluctuations and the limit of predictability in protein evolution
• The effects of external noise on threshold induced correlations in ferromagnetic systems
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Revisiting the single-saddle model for the $\beta$-relaxation of supercooled liquids
• Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment
• Logarithmic critical slowing down in complex systems: from statics to dynamics
• Microscopic Theory of a Fluctuation-Induced Dynamical Crossover in Supercooled Liquids
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain