Abstract
The profiles of the order parameter and of other local densities in confined systems at the bulk critical temperature are considered. For a great variety of two-dimensional confined geometries and for spherical boundaries in general dimension d, conformal invariance completely determines the functional form of the profile when a uniform scale-invariant boundary condition is imposed. The analytic expression for the profile in a two-dimensional strip of semi-infinite length and finite width implies the surface scaling dimension x s = 2. The exact magnetization profile in an Ising strip at the bulk critical temperature with spins on opposite edges fixed in opposing directions is derived with conformal-invariance methods.
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