Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses

Abstract

The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of different models on sparse and dense graphs. These models exhibit very diverse behaviors, and an asymptotic extrapolation is often complicated by higher-order corrections. The clearest picture, in fact, emerges from the study of graph-bipartitioning, a combinatorial optimization problem closely related to spin glasses. Aside from two-spin interactions with discrete bonds, we also consider problems with Gaussian bonds and three-spin interactions, which behave differently to a significant degree.

Much extended version, comparing fluctuations for SK and five other models. Now 20 RevTex-pages, 10 tables, 27 figures

References in corpus (15)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Universality in the level statistics of disordered systems
• Universality-class dependence of energy distributions in spin glasses
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Conjecture on the maximum cut and bisection width in random regular graphs
• Probing tails of energy distributions using importance-sampling in the disorder with a guiding function
• Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
• Matching between typical fluctuations and large deviations in disordered systems : application to the statistics of the ground state energy in the SK spin-glass model
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model
• Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass
• Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds
• Reduction of Dilute Ising Spin Glasses
• Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass

Cited by in corpus (15)

• Hybrid Quantum Annealing via Molecular Dynamics
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Inability of a graph neural network heuristic to outperform greedy algorithms in solving combinatorial optimization problems like Max-Cut
• Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• Finite size corrections in the random energy model and the replica approach
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• 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
• Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Suzuki-Kubo Mean-field Ising Dynamics
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization
• Ground States of the Mean-Field Spin Glass with 3-Spin Couplings