Abstract
We prove that the three-dimensional Ising model in a random magnetic field exhibits long-range order at zero temperature and small disorder. Hence the lower critical dimension for this model is two (or less) and not three as has been suggested by some.
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Communicated by A. Jaffe
Junior Fellow, Society of Fellows. Research supported in part by the National Science Foundation under Grant PHY82-03669
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Imbrie, J.Z. The ground state of the three-dimensional random-field Ising model. Commun.Math. Phys. 98, 145–176 (1985). https://doi.org/10.1007/BF01220505
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DOI: https://doi.org/10.1007/BF01220505