Surface thermodynamic functions of the Ising model from a renormalization group

Abstract

The surface thermodynamic functions of the semi-infinite square and simple-cubic s=½ nearest-neighbor Ising models are computed numerically from renormalization groups based on simple cell clusters. It is shown how the exact high- and low-temperature limits may be incorporated into the calculations by (i) building in proper site coordination via an Ursell expansion for the free energy and (ii) treating the ground state exactly. In d=2 a 4 × 4 cell-cluster approximation is in excellent agreement with the exact results of Fisher and Ferdinand. In d=3 a 2 × 8 cell-cluster approximation gives plausible results with enough structure to be interesting.