BOUNDARY AND FINITE-SIZE EFFECTS IN 2-DIMENSIONAL STRUCTURE FACTORS AT CRITICALITY

We show how the apparent power-law scaling of classical two-dimensiona l structure factors in bounded domains at criticality is related to fi xed and free boundary conditions on the order parameter. This enables us to predict the behavior of the corresponding apparent scaling dimen sions based on a simple symmetry analysis. With the use of correlation functions froin conformal field theory, our predictions are confirmed with exact calculations for multicritical Ising models. Effects of ra ndom boundary fields are also discussed.