  We compute for various perturbed conformal field theories the vacuum energies
by means of the thermodynamic Bethe ansatz. Depending on the infrared and
ultraviolet divergencies of the models, governed by the scaling dimensions of
the underlying perturbed conformal field theory in the ultraviolet, the vacuum
energies exhibit different types of characteristics. In particular, for the
homogeneous sine-Gordon models we observe that once the conformal dimension of
the perturbing scalar field is smaller or greater than 1/2, the vacuum energies
are positive or negative, respectively. This behaviour indicates the need for
additional ultraviolet counterterms in the latter case. At the transition
points we obtain an infinite vacuum energy, which is partly explainable with
the presence of several free Fermions in the models studied.
