### Abstract

A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.

Original language | English (US) |
---|---|

Pages (from-to) | 2561-2562 |

Number of pages | 2 |

Journal | Journal of Mathematical Physics |

Volume | 32 |

Issue number | 9 |

State | Published - 1991 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*32*(9), 2561-2562.

**The effective field approximation for Ising spin glasses on simply connected lattices.** / Zhang, Guihua; Percus, Jerome.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 32, no. 9, pp. 2561-2562.

}

TY - JOUR

T1 - The effective field approximation for Ising spin glasses on simply connected lattices

AU - Zhang, Guihua

AU - Percus, Jerome

PY - 1991

Y1 - 1991

N2 - A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.

AB - A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.

UR - http://www.scopus.com/inward/record.url?scp=36449008439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36449008439&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 2561

EP - 2562

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

ER -