The local magnetization in a semi-infinite planar Ising ferromagnet with an edge field H₁ is examined as a function of distance from the edge. The asymptotic form of this magnetization profile for distances large compared to the bulk correlation length has a nontrivial dependence on the edge field. The exact scaling function for this dependence in the limit of small edge field can be derived from a simple droplet argument.
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Abraham et al. (1988) studied this question.
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