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The ground state of the three-dimensional random-field Ising model. (English) Zbl 1223.82016
Summary: 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.

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
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