### Abstract

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of δ functions at [Formula Presented] This rules out the nonstandard mean-field picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the possibility of even limited versions of mean-field ordering in realistic spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes.

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

Pages (from-to) | 1356-1366 |

Number of pages | 11 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 57 |

Issue number | 2 |

DOIs | |

State | Published - 1998 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics