The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm

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Abstract

Ground states of three-dimensional Edwards-Anderson ±J Ising spin glasses were calculated with a hybrid of genetic algorithm and local optimization. The algorithm was fast and reliable enough to allow extensive calculations for systems of linear size between 3 and 14 and determination of the average ground state energies with small errors. A linear dependence on 1/volume approximates the data very accurately in the whole range. The -1.7863 ± 0.0004 value for the ground state energy per spin of the infinite system was determined with extrapolation. The main source of uncertainty is that the functional form of the small but significant deviation from the linear 1/volume dependence is unknown.

Original languageEnglish
Pages (from-to)283-292
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Volume223
Issue number3-4
Publication statusPublished - Jan 15 1996

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Hybrid Genetic Algorithm
Ground State Energy
Spin Glass
Ising
genetic algorithms
spin glass
Linear dependence
Local Optimization
ground state
Infinite Systems
Extrapolation
Ground State
Deviation
Genetic Algorithm
Uncertainty
Unknown
Three-dimensional
energy
extrapolation
Range of data

Keywords

  • Genetic algorithm
  • Ground state
  • Ising spin glass

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

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N2 - Ground states of three-dimensional Edwards-Anderson ±J Ising spin glasses were calculated with a hybrid of genetic algorithm and local optimization. The algorithm was fast and reliable enough to allow extensive calculations for systems of linear size between 3 and 14 and determination of the average ground state energies with small errors. A linear dependence on 1/volume approximates the data very accurately in the whole range. The -1.7863 ± 0.0004 value for the ground state energy per spin of the infinite system was determined with extrapolation. The main source of uncertainty is that the functional form of the small but significant deviation from the linear 1/volume dependence is unknown.

AB - Ground states of three-dimensional Edwards-Anderson ±J Ising spin glasses were calculated with a hybrid of genetic algorithm and local optimization. The algorithm was fast and reliable enough to allow extensive calculations for systems of linear size between 3 and 14 and determination of the average ground state energies with small errors. A linear dependence on 1/volume approximates the data very accurately in the whole range. The -1.7863 ± 0.0004 value for the ground state energy per spin of the infinite system was determined with extrapolation. The main source of uncertainty is that the functional form of the small but significant deviation from the linear 1/volume dependence is unknown.

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