Finitely coordinated models for low-temperature phases of amorphous systems

Abstract

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behavior of finite dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von-Karman type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well known universal glassy low temperature anomalies when quantum effects are taken into account.

35 pages, 8 Figures

References in corpus (28)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• The Bethe lattice spin glass revisited
• The structural glass transition and the entropy of the metastable states
• Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
• Thermodynamics of glasses: a first principle computation
• Recipes for metastable states in Spin Glasses
• Phase diagram of glassy systems in an external field
• Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior
• Lattice Glass Models
• Replica Field Theory for Deterministic Models: Binary Sequences with Low Autocorrelation
• Glass models on Bethe lattices
• Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
• A ferromagnet with a glass transition
• Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
• From Large Scale Rearrangements to Mode Coupling Phenomenology
• Random Matrix Approach to Glassy Physics --- Low Temperatures and Beyond
• Glassy behavior induced by geometrical frustration in a hard-core lattice gas model
• Random Graph Coloring - a Statistical Physics Approach
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs
• Dynamics of dilute disordered models: a solvable case
• Universality in Glassy Low-Temperature Physics
• Towards finite-dimensional gelation
• Elastic heterogeneity of soft random solids
• A hard-sphere model on generalized Bethe lattices: Statics
• A hard-sphere model on generalised Bethe lattices: Dynamics
• Cavity Approach to the Random Solid State
• Translational Invariance in Models for Low-Temperature Properties of Glasses

Cited by in corpus (15)

• Spectra of Sparse Random Matrices
• Cavity and replica methods for the spectral density of sparse symmetric random matrices
• Localization and universality of eigenvectors in directed random graphs
• A unifying model for random matrix theory in arbitrary space dimensions
• Spin models on random graphs with controlled topologies beyond degree constraints
• Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
• Impact of jamming criticality on low-temperature anomalies in structural glasses
• Top Eigenpair Statistics for Weighted Sparse Graphs
• Second largest Eigenpair Statistics for Sparse Graphs
• Localization in random bipartite graphs: numerical and empirical study
• Imaginary replica analysis of loopy regular random graphs
• Soft modes in vector spin glass models on sparse random graphs
• Replica theory for learning curves for Gaussian processes on random graphs
• Sparse Random Block Matrices
• Top eigenpair statistics of diluted Wishart matrices