The square lattice Ising model with a free surface

Using the appropriately generalised finite lattice method, series expansions of the layer ( chi ₁) and local ( chi ₁₁) susceptibilities of the square lattice Ising model have been obtained. They extend existing series by 3 and 13 terms for chi ₁ and chi ₁₁, respectively. Series analysis yields the exponent estimates gamma ₁=1.375+or-0.005 and gamma ₁₁=0.00+or-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 gamma ₁₁=v-1 for the square lattice self-avoiding walk problem found in an earlier study.