Random elastic networks : strong disorder renormalization approach

Abstract

For arbitrary networks of random masses connected by random springs, we define a general strong disorder real-space renormalization (RG) approach that generalizes the procedures introduced previously by Hastings [Phys. Rev. Lett. 90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601 (2010)] respectively. The principle is to eliminate iteratively the elementary oscillating mode of highest frequency associated with either a mass or a spring constant. To explain the accuracy of the strong disorder RG rules, we compare with the Aoki RG rules that are exact at fixed frequency.

8 pages, v2=final version

References in corpus (68)

• Statistical mechanics of complex networks
• Self-similarity of complex networks
• Origins of fractality in the growth of complex networks
• Strong disorder RG approach of random systems
• Entanglement entropy of random quantum critical points in one dimension
• How to calculate the fractal dimension of a complex network: the box covering algorithm
• Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
• Localization of maximal entropy random walk
• Small world-Fractal Transition in Complex Networks: Renormalization Group Approach
• Griffiths phases on complex networks
• Strong disorder fixed point in absorbing state phase transitions
• Fractality in complex networks: critical and supercritical skeletons
• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Absorbing state phase transitions with quenched disorder
• Critical behavior and Griffiths effects in the disordered contact process
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Phase transition of one dimensional bosons with strong disorder
• Effects of dissipation on a quantum critical point with disorder
• Criticality and entanglement in random quantum systems
• Heat transport and phonon localization in mass-disordered harmonic crystals
• Infinite-randomness quantum critical points induced by dissipation
• Theory of smeared quantum phase transitions
• Superfluid-insulator transition of disordered bosons in one-dimension
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Complex networks renormalization: flows and fixed points
• Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
• Localization, anomalous diffusion and slow relaxations: a random distance matrix approach
• Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks
• Partially asymmetric exclusion models with quenched disorder
• The insulating phases and superfluid-insulator transition of disordered boson chains
• Anderson localization of phonons in dimension $d=1,2,3$ : finite-size properties of the Inverse Participation Ratios of eigenstates
• Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions
• Entanglement entropy of the random spin-1 Heisenberg chain
• Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature
• Partially Asymmetric Exclusion Processes with Sitewise Disorder
• Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
• Strong Randomness Fixed Point in the Dissipative Random Transverse Field Ising Model
• Localization properties of the anomalous diffusion phase $x{t}^{\mu }$ in the directed trap model and in the Sinai diffusion with bias
• Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Reaction Diffusion Models in One Dimension with Disorder
• The partially asymmetric zero range process with quenched disorder
• Excitations of the One Dimensional Bose-Einstein Condensates in a Random Potential
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Disorder-Induced Vibrational Localization
• Renormalization flows in complex networks
• Interaction-dependent enhancement of the localisation length for two interacting particles in a one-dimensional random potential
• Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains
• Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain
• Energy dynamics in the Sinai model
• Sinai model in presence of dilute absorbers
• Renormalization Group Approach to Oscillator Synchronization
• Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
• Statistics of the two-point transmission at Anderson localization transitions
• Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
• Universality in the one-dimensional chain of phase-coupled oscillators
• Random Vibrational Networks and Renormalization Group
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Strongly disordered Hubbard model in one dimension: spin and orbital infinite randomness and Griffiths phases
• The various facets of random walk entropy
• Griffiths-McCoy singularities in random quantum spin chains: Exact results
• Anomalous diffusion in disordered multi-channel systems

Cited by in corpus (10)

• Strong Disorder RG approach - a short review of recent developments
• Emergent percolation length and localization in random elastic networks
• Maximal entropy random walk in community finding
• Spectral analysis and slow spreading dynamics on complex networks
• Slow, bursty dynamics as the consequence of quenched network topologies
• Exact Solution for Statics and Dynamics of Maximal Entropy Random Walk on Cayley Trees
• A critical Dyson hierarchical model for the Anderson localization transition
• Localization transition, Lifschitz tails and rare-region effects in network models
• Maximal-entropy random walk unifies centrality measures
• Slow dynamics of the contact process on complex networks