Constructing explicit magnetic analogies for the dynamics of glass forming liquids

Abstract

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

References in corpus (15)

• Theory of Structural Glasses and Supercooled Liquids
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• The structural glass transition and the entropy of the metastable states
• Fragilities of Liquids Predicted from the Random First Order Transition Theory of Glasses
• Thermodynamics of glasses: a first principle computation
• Recipes for metastable states in Spin Glasses
• The Shapes of Cooperatively Rearranging Regions in Glass Forming Liquids
• Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Theory of Aging in Structural Glasses
• Activated events in glasses: the structure of entropic droplets
• Droplets and the configurational entropy crisis for random first order transitions
• Glass Phenomenology from the Connection to Spin Glasses
• A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition
• Spin Glass Theory: numerical and experimental results in three-dimensional systems

Cited by in corpus (23)

• Mean field theory of hard sphere glasses and jamming
• Perspective: The Glass Transition
• Ideal Glass Transitions by Random Pinning
• A universal origin for secondary relaxations in supercooled liquids and structural glasses
• The Ultimate Fate of Supercooled Liquids
• Theory of the Structural Glass Transition: A Pedagogical Review
• Evidence for a disordered critical point in a glass-forming liquid
• Random-field-like criticality in glass-forming liquids
• Self-induced heterogeneity in deeply supercooled liquids
• Random-field Ising and $O(N)$ models: Theoretical description through the functional renormalization group
• Domain walls and Schramm-Loewner evolution in the random-field Ising model
• Stress distribution and the fragility of supercooled melts
• Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models
• Real Space Renormalization Group Theory of Disordered Models of Glasses
• Random-Field Ising like effective theory of the glass transition: I Mean-Field Models
• Scaling and universality in glass transition
• Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• The Interplay of Nonlinearity and Architecture in Equilibrium Cytoskeletal Mechanics
• Fluctuations and Shape of Cooperative Rearranging Regions in Glass-Forming Liquids
• Microscopic theory of the glassy dynamics of passive and active network materials
• Pressure in the Landau-Ginzburg Functional: Pascal's Law, Nucleation in Fluid Mixtures, a Meanfield Theory of Amphiphilic Action, and Interface Wetting in Glassy Liquids
• Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope