Abstract
The two-dimensional anisotropie, nearest-neighbor Heisenberg model on a square lattice, both quantum and classical, has been shown rigorously to have a phase transition in the sense that the spontaneous magnetization is positive at low temperatures. This is so for all anisotropies. An analogous result (staggered polarization) holds for the antiferromagnet in the classical case; in the quantum case it holds if the anisotropy is large enough (depending on the single-site spin).
A. P. Sloan Foundation Fellow; partially supported by U. S. National Science Foundation, Grant No. MPS7511864.
Work partially supported by U. S. National Science Foundation, Grant No. MCS 75-21684 A01.
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Reference
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Absence of a phase transition in the classical model for a =0 follows from a result of O. McBryan and T. Spencer (to be published). 442
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Fröhlich, J., Lieb, E.H. (1977). Existence of Phase Transitions for Anisotropic Heisenberg Models. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_10
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