Abstract
A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity isnot proved, but for which the rest of the proof is valid.
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Communicated by J. Glimm
Work partially supported by U.S. National Science Foundation grant no. MPS 75-11864
Work partially supported by U.S. National Science Foundation grant no. MCS 75-21684 A01
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Fröhlich, J., Lieb, E.H. Phase transitions in anisotropic lattice spin systems. Commun.Math. Phys. 60, 233–267 (1978). https://doi.org/10.1007/BF01612891
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DOI: https://doi.org/10.1007/BF01612891