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The lower critical dimension for a random-field Ising model cooled from the paramagnetic region is found to be 4, although it is 2 at equilibrium. The coherence length R is proportional to H^{-₇}f (t), where H is the random-field amplitude and t is the time. At low temperature, ₇=2 and f (t) =ln (t). At the transition temperature T₂₀ of the pure system, ₇1 and f (t) =1. The agreement with experiment is acceptable.
Jacques Villain (Mon,) studied this question.
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