CONFORMAL THEORY OF THE 2-DIMENSIONAL O(N) MODEL WITH ORDINARY, EXTRAORDINARY, AND SPECIAL BOUNDARY-CONDITIONS

The two-dimensional critical O(N) model with ordinary, extraordinary, and special boundary conditions is analyzed with conformal-invariance methods. Contrary to an earlier conjecture, the energy density does not vanish at an edge with special boundary conditions. Exact expressions for the energy-energy correlation function in the half-space are given for all three boundary conditions. For several sets of mixed boundary conditions the Casimir contribution to the free energy in the strip geometry and the profile of the energy density are calculated.