Spin glasses and algorithm benchmarks: A one-dimensional view

Abstract

Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore large-scale numerical simulations are the tool of choice. Concepts and algorithms derived from the study of spin glasses have been applied to diverse fields in computer science and physics. In this work a one-dimensional long-range spin-glass model with power-law interactions is discussed. The model has the advantage over conventional systems in that by tuning the power-law exponent of the interactions the effective space dimension can be changed thus effectively allowing the study of large high-dimensional spin-glass systems to address questions as diverse as the existence of an Almeida-Thouless line, ultrametricity and chaos in short range spin glasses. Furthermore, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.

10 pages, 8 figures (two in crappy quality due to archive restrictions). Proceedings of the International Workshop on Statistical-Mechanical Informatics 2007, Kyoto (Japan) September 16-19, 2007

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Cited by in corpus (13)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models
• 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
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Analysis of Evolutionary Algorithms on the One-Dimensional Spin Glass with Power-Law Interactions