Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions

Abstract

Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both finite-temperature and ground-state studies are carried out. For the range of sizes studied the data cannot be fitted to any of the standard spin-glass scenarios without including corrections to scaling. Incorporating such corrections we find that the fractal dimension of the surface of the excitations, is either equal to the space dimension, consistent with replica symmetry breaking, or very slightly less than it. The latter case is consistent with the droplet and "trivial-nontrivial" (TNT) pictures.

7 pages, 6 figures, 8 tables

References in corpus (2)

• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo

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• Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Local field distributions in spin glasses
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass