### Abstract

We propose a test to distinguish, both numerically and theoretically, between the two competing pictures of short-ranged Ising spin glasses at low temperature: chaotic size dependence. Scaling theories in which at most two pure states (related by a global spin flip) occur require that finite-volume correlations (with, say, periodic boundary conditions) have a well-defined thermodynamic limit. We argue, however, that the picture based on the infinite-ranged Sherrington-Kirkpatrick model, with many noncongruent pure states, leads to a breakdown of the thermodynamic limit. The argument combines rigorous and heuristic elements; one of the fomer is a proof that in the infinite-ranged model itself, non-self-averaging implies chaotic size dependence. Numerical tests, based on chaotic size dependence, could provide a more sensitive measure than the usual overlap distribution P(q) in determining the number of pure states.

Original language | English (US) |
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Pages (from-to) | 973-982 |

Number of pages | 10 |

Journal | Physical Review B |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - 1992 |

### ASJC Scopus subject areas

- Condensed Matter Physics

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## Cite this

*Physical Review B*,

*46*(2), 973-982. https://doi.org/10.1103/PhysRevB.46.973