## Abstract

We consider Ising spin glasses on Z^{d} with couplings J_{xy}=c_{y-x}Z_{xy}, where the c_{y}'s are nonrandom real coefficients and the Z_{xy}'s are independent, identically distributed random variables with E[Z_{xy}]=0 and E[Z_{xy}^{2}]=1. We prove that if ∑_{y}|c_{y}|=∞ while ∑_{y}|c_{y}|^{2}=∞, then (with probability one) there are uncountably many (infinite volume) ground states {Mathematical expression}, each of which has the following property: for any temperature T<∞, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from {Mathematical expression} only at finitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.

Original language | English (US) |
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Pages (from-to) | 371-387 |

Number of pages | 17 |

Journal | Communications In Mathematical Physics |

Volume | 157 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1993 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics