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.
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© 1988 Springer-Verlag Berlin Heidelberg
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Kennedy, T., Lieb, E.H., Shastry, B.S. (1988). Existence of Néel Order in Some Spin-1/2 Heisenberg Antiferromagnets. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_16
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DOI: https://doi.org/10.1007/978-3-662-10018-9_16
Publisher Name: Springer, Berlin, Heidelberg
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