The square lattice Ising model with a free surface

Abstract

Using the appropriately generalised finite lattice method, series expansions of the layer (χ1) and local (χ11) susceptibilities of the square lattice Ising model have been obtained. They extend existing series by 3 and 13 terms for χ1 and χ11, respectively. Series analysis yields the exponent estimates γ1 = 1·375±0·005 and γ11 = 0·00±0·01, in agreement with scaling predictions. Repetition of the analysis used in the analogous self-avoiding walk problem confirms the breakdown of the renormalisation group scaling relation γ11 = v − 1 for the square lattice self-avoiding walk problem found in an earlier study. © 1980 The Institute of Physics.