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.