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

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

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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
Issue number5-6
StatePublished - Dec 1988

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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


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