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We use a real-space renormalization transformation with a cumulant expansion, modified to include free-surface boundary conditions, to study the critical behavior of semi-infinite ferromagnetic systems. We present first-order calculations for the Ising model on the semi-infinite square and simple cubic lattices. Our results serve as the basis of a critical discussion of previous real-space and momentum-space renormalization-group calculations.
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Dunfield et al. (1980) studied this question.
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