Critical exponents in the presence of a tip

The behavior of Landau-Ginzburg model of a critical system, appropriate to describe SAW polymers, in the presence of a conical boundary is studied within mean field and by epsilon expansion in d=4-epsilon dimensions. New exponents emerge for correlation functions near the boundaries, in this case the tip of the cone. In the limit of a sharp cone we find a new exponent which we interpret for a SAW polymer by using its fractal dimension.