The ordered phase of the one-dimensional Ising spin glass with long-range interactions

Abstract

The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar, Anderson and Stein have been re-examined and a new fixed point has been found. The fixed points which have previously been studied are found to be inappropriate. It is shown that the renormalization group equations themselves directly imply that the spin glass phase is replica symmetric, in agreement with droplet model expectations, when the range exponent $\sigma$ lies between the upper and lower critical values.

9 pages, no figures.

References in corpus (5)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Ultrametricity and clustering of states in spin glasses: A one-dimensional view

Cited by in corpus (19)

• Disappearance of the de Almeida-Thouless line in six dimensions
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• One-dimensional infinite component vector spin glass with long-range interactions
• Phase Transitions in the 1-d Long-Range Diluted Heisenberg Spin Glass
• Study of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg Spin Glasses
• Spin glasses in the non-extensive regime
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• Ultrametric probe of the spin-glass state in a field
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Chaos properties of the one-dimensional long-range Ising spin-glass
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Stability of the replica-symmetric saddle-point in general mean-field spin-glass models
• Numerical study of the dynamics of some long range spin glass models
• Relaxational processes in the one-dimensional Ising model with long-range interactions
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Order parameter for non-mean-field spin glasses