DENSITY PROFILES IN CONFINED CRITICAL SYSTEMS AND CONFORMAL-INVARIANCE

The conformal-invariance approach is extended to two-dimensional critical systems with mixed ab boundary conditions. The profiles <phi(r)>ab of the magnetization and the energy density in Ising and Q-state Potts strips with +- and fixed-free boundary conditions are derived. The profile of an arbitrary operator degenerate at level 2 is expressed in terms of hypergeometric functions. The universal amplitudes A(ab), B(ab) of the Casimir force and the Fisher-de Gennes distant-wall correction to the profile satisfy B(ab) = -4-pi-x-phi-C-1A(ab). Here x-phi is the scaling dimension of phi(r), and c is the central charge.