Energetics and geometry of excitations in random systems

Abstract

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.

4 pages, eps files included

References in corpus (8)

• Nature of the Spin Glass State
• Spin and link overlaps in 3-dimensional spin glasses
• Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder
• The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass
• A geometrical picture for finite dimensional spin glasses
• Thermodynamics of Mesoscopic Vortex Systems in 1+1 Dimensions
• Fractal Droplets in Two Dimensional Spin Glasses
• Simulation of the Zero Temperature Behavior of a 3-Dimensional Elastic Medium

Cited by in corpus (35)

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• Hysteretic Optimization
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Stiffness Exponents for Lattice Spin Glasses in Dimensions d=3,...,6
• Fractal dimension of domain walls in two-dimensional Ising spin glasses
• Low-Temperature Excitations of Dilute Lattice Spin Glasses
• Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Domain-wall excitations in the two-dimensional Ising spin glass
• Ground states of two-dimensional $\pm$J Edwards-Anderson spin glasses
• Interfaces (and Regional Congruence?) in Spin Glasses
• Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• Monte Carlo simulations of spin glasses at low temperatures: Effects of free boundary conditions
• Non-perturbative effects in spin glasses
• Low Energy Excitations in Spin Glasses from Exact Ground States
• Domain walls and chaos in the disordered SOS model
• Evidence for universal scaling in the spin-glass phase
• Generating droplets in two-dimensional Ising spin glasses by using matching algorithms
• The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions
• First excitations in two- and three-dimensional random-field Ising systems
• Determining Energy Barriers by Iterated Optimization: The Two-Dimensional Ising Spin Glass
• Backbone structure of the Edwards-Anderson spin-glass model
• Ground State Stability and the Nature of the Spin Glass Phase
• Fractal dimension of spin glasses interfaces in dimensions $d=2$ and $d=3$ via strong disorder renormalization at zero temperature
• Reduction of Two-Dimensional Dilute Ising Spin Glasses
• Numerical results for the Edwards-Anderson spin-glass model at low temperature
• Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain walls
• On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
• The Effect of Pure State Structure on Nonequilibrium Dynamics
• Configuration Memory in Patchwork Dynamics for Low-dimensional Spin Glasses
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman