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

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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 ber 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.

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Author notes

  1. B. Sriram Shastry

    Present address: Tata Institute of Fundamental Research, Bombay, India

Authors and Affiliations

  1. Department of Physics, Princeton University, 08544, Princeton, New Jersey

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

Authors
  1. Tom Kennedy
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  2. Elliott H. Lieb
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  3. B. Sriram Shastry
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Kennedy, T., Lieb, E.H. & Shastry, B.S. Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets. J Stat Phys 53, 1019–1030 (1988). https://doi.org/10.1007/BF01023854

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  • DOI: https://doi.org/10.1007/BF01023854

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