  We present energy and free energy analyses on all variational schemes used in
the spin-boson model at both T=0 and $T\neq0$. It is found that all the
variational schemes have fail points, at where the variational schemes fail to
provide a lower energy (or a lower free energy at $T\neq0$) than the
displaced-oscillator ground state and therefore the variational ground state
becomes unstable, which results in a transition from a variational ground state
to a displaced oscillator ground state when the fail point is reached. Such
transitions are always misidentied as crossover from a delocalized to localized
phases in variational calculations, leading to an artifact of phonon-induced
localization. Physics origin of the fail points and explanations for different
transition behaviors with different spectral functions are found by studying
the fail points of the variational schemes in the single mode case.
