Exotic states in long-range spin glasses

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)371-387
Number of pages17
JournalCommunications In Mathematical Physics
Volume157
Issue number2
DOIs
StatePublished - Oct 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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