Star–triangle approach to boundary behavior in the two-dimensional Ising model

Hilhorst and van Leeuwen showed how to calculate boundary properties of the Ising model on the triangular lattice by iterating a mapping based on the star–triangle transformation. We apply this approach to the Ising model with homogeneous initial couplings in both the semi-infinite and strip geometries. Several exact results for the boundary correlation length and the magnetization are reproduced. The correlation-dimensionality transition for enhanced edge couplings (dual of Abraham’s interface-unbinding transition) is also considered.