  We compute the continuum limit of the spectra for the XX-model with arbitrary
complex boundary fields. In the case of hermitian boundary terms one obtains
the partition functions of the free compactified boson field on a cylinder with
Neumann-Neumann, Dirichlet-Neumann or Dirichlet-Dirichlet boundary conditions.
This applies also for certain non-hermitian boundaries. For special cases we
also compute the free surface energy. For certain non-hermitian boundary terms
the results are more complex.Here one obtains logarithmic corrections to the
free surface energy. The asymmetric version of the XX-model with boundaries
(this includes the Dzyaloshinsky-Moriya interaction)is also discussed.
