Universal critical-point amplitudes in parallel-plate geometries

Abstract

In a critical system contained between parallel plates, it is known that the magnetization and energy density profiles close to one wall are modified due to the presence of the other wall. In addition, there is a long-range force between the walls. It is shown that the ratios of the ampiltudes governing these effects are universal, and moreover, independent of the boundary conditions at either wall. Their values are proportional to the scaling dimension of the density under consideration. Results are also given for the effects of local curvature of the wall on the density profiles. These results are shown to be a consequence of the conformal invariance of the critical system.