Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets

Tom Kennedy, Elliott H. Lieb, B. Sriram Shastry

Research output: Contribution to journalArticle

123 Scopus citations

Abstract

The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to be r times its value in the other two lattice directions. We prove the existence of Néel order for 0.16≤r≤1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.

Original languageEnglish (US)
Pages (from-to)1019-1030
Number of pages12
JournalJournal of Statistical Physics
Volume53
Issue number5-6
DOIs
StatePublished - Dec 1 1988
Externally publishedYes

Keywords

  • Gaussian domination
  • Néel order
  • infrared bounds
  • spin-1/2 antiferromagnets

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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