Exotic states in long-range spin glasses

Research output: Contribution to journalArticle

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

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Spin Glass
spin glass
Gibbs States
Disordered Systems
random variables
Ising
Identically distributed
Range of data
Ground State
Random variable
boundary conditions
Boundary conditions
Configuration
ground state
Dependent
Coefficient
coefficients
configurations
temperature

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 157, No. 2, 10.1993, p. 371-387.

Research output: Contribution to journalArticle

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