Crossover function for the local susceptibility of a semi-infinite system near the special transition

The crossover function associated with the local susceptibility χ₁₁ near the multicritical point of a semi-infinite system is calculated to O(ε). As the temperature decreases towards its critical value, the effective exponent γ₁₁ changes from a value γ₁₁⁰ characteristic of the special transition to a value γ₁₁^∞ characteristic of the ordinary transition.