Correlation functions of semi-infinite two-dimensional Ising model. III. Influence of a “fixed” boundary

Exact calculations for the semi-infinite two-dimensional Ising model are used to analyze the influence of an external field applied to the boundary on the distribution of the profile of the local magnetization. It is shown that near the critical point the local magnetization takes a scale-invariant form. The behavior of the scaling function for different values of the field and distances to the boundary is studied.