Hysteretic Optimization For Spin Glasses

Abstract

The recently proposed Hysteretic Optimization (HO) procedure is applied to the 1D Ising spin chain with long range interactions. To study its effectiveness, the quality of ground state energies found as a function of the distance dependence exponent, $\sigma$, is assessed. It is found that the transition from an infinite-range to a long-range interaction at $\sigma =0.5$ is accompanied by a sharp decrease in the performance . The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite-range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way auto-correlations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.

6 pages, 9 figures. To appear in JSTAT. Author website: http://www.bgoncalves.com

References in corpus (10)

• Simulated Tempering: A New Monte Carlo Scheme
• Optimization with Extremal Dynamics
• Nature's Way of Optimizing
• Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Extremal Optimization for Sherrington-Kirkpatrick Spin Glasses
• Probing the Almeida-Thouless line away from the mean-field model
• Hysteretic Optimization
• Hysteretic optimization for the Sherrington-Kirkpatrick spin glass
• Is demagnetization an efficient optimization method?

Cited by in corpus (6)

• Self-Organized Criticality in Glassy Spin Systems Requires a Diverging Number of Neighbors
• Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Self-organized critical behavior and marginality in Ising spin glasses
• Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias
• Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses