### 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) |
---|---|

Pages (from-to) | 371-387 |

Number of pages | 17 |

Journal | Communications in Mathematical Physics |

Volume | 157 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1993 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*157*(2), 371-387. https://doi.org/10.1007/BF02099766

**Exotic states in long-range spin glasses.** / Gandolfi, Alberto; Newman, Charles; Stein, D. L.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 157, no. 2, pp. 371-387. https://doi.org/10.1007/BF02099766

}

TY - JOUR

T1 - Exotic states in long-range spin glasses

AU - Gandolfi, Alberto

AU - Newman, Charles

AU - Stein, D. L.

PY - 1993/10

Y1 - 1993/10

N2 - We consider Ising spin glasses on Zd with couplings Jxy=cy-xZxy, where the cy's are nonrandom real coefficients and the Zxy's are independent, identically distributed random variables with E[Zxy]=0 and E[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|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.

AB - We consider Ising spin glasses on Zd with couplings Jxy=cy-xZxy, where the cy's are nonrandom real coefficients and the Zxy's are independent, identically distributed random variables with E[Zxy]=0 and E[Zxy2]=1. We prove that if ∑y|cy|=∞ while ∑y|cy|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.

UR - http://www.scopus.com/inward/record.url?scp=21344494954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344494954&partnerID=8YFLogxK

U2 - 10.1007/BF02099766

DO - 10.1007/BF02099766

M3 - Article

VL - 157

SP - 371

EP - 387

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -