Real-space renormalization-group transformation for semi-infinite Ising systems

Abstract
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.