  Using exact calculations, we elucidate the significance of the surface
(bound) states for the thermal Casimir interactions for an Ising strip with a
finite width. The surface state arises whenever an imaginary wavenumber mode
appears in the spectrum of the transfer matrix, taken in the direction parallel
to the edges of the strip. Depending on the boundary conditions, the imaginary
modes emerge below or above the bulk critical temperature, or below the wetting
temperature of a single surface with surface magnetic field. The bound states
are responsible for the strong asymmetry of the Casimir forces between the
super- and sub-critical regimes and for their sign. Our analysis uses the fact
that the Casimir forces have two mathematical forms. We show that these very
different representation are the same and in the process find the origin of the
asymmetry.
