### 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 language | English |
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Pages (from-to) | 283-292 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 223 |

Issue number | 3-4 |

Publication status | Published - Jan 15 1996 |

### Fingerprint

### Keywords

- Genetic algorithm
- Ground state
- Ising spin glass

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm.** / Pál, K.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 223, no. 3-4, pp. 283-292.

}

TY - JOUR

T1 - The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm

AU - Pál, K.

PY - 1996/1/15

Y1 - 1996/1/15

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.

KW - Genetic algorithm

KW - Ground state

KW - Ising spin glass

UR - http://www.scopus.com/inward/record.url?scp=0000538696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000538696&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000538696

VL - 223

SP - 283

EP - 292

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -