Large deviations in spin-glass ground-state energies

Abstract

The ground-state energy E_0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be understood qualitatively, in particular with the help of semi-analytical results for hierarchical lattices. Particular attention is paid to the Sherrington-Kirkpatrick model; after comparing to the Tracy-Widom distribution which follows from the spherical approximation, we find that the large deviations give rise to non-trivial scaling laws with N.

11 pages, 12 figures, extended discussion, clarifications and references

References in corpus (3)

• Energy exponents and corrections to scaling in Ising spin glasses
• Probability distribution of the free energy of a directed polymer in a random medium
• Renormalization for Discrete Optimization

Cited by in corpus (28)

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• Universality-class dependence of energy distributions in spin glasses
• Phase diagram and large deviations in the free-energy of mean-field spin-glasses
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Probing tails of energy distributions using importance-sampling in the disorder with a guiding function
• Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses
• Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
• One-dimensional infinite component vector spin glass with long-range interactions
• Universality and Deviations in Disordered Systems
• Spin glasses and algorithm benchmarks: A one-dimensional view
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• Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy
• Numerical estimate of finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass
• 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
• Chaos properties of the one-dimensional long-range Ising spin-glass
• Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Large deviations of the free energy in the p-spin glass spherical model
• Replica-symmetry breaking transitions in the large deviations of the ground-state of a spherical spin-glass
• Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass
• Study of longitudinal fluctuations of the Sherrington-Kirkpatrick model