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.

arXiv comment7 pages, 6 figures, 8 tables

References in corpus (19)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Nature of the Spin Glass State
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Spin and link overlaps in 3-dimensional spin glasses
• Lower Critical Dimension of Ising Spin Glasses
• The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Scaling of stiffness energy for 3d +/-J Ising spin glasses
• Triviality of the Ground State Structure in Ising Spin Glasses
• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses
• Large-scale low-energy excitations in 3-d spin glasses
• Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
• A geometrical picture for finite dimensional spin glasses
• Low Energy Excitations in Spin Glasses from Exact Ground States
• Nature of the Spin-glass State in the Three-dimensional Gauge Glass
• Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures

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