  A (1+1)-dimensional quantum field theory with a degenerate vacuum (in
infinite volume) can contain particles, known as kinks, which interpolate
between different vacua and have nontrivial restrictions on their
multi-particle Hilbert space. Assuming such a theory to be integrable, we show
how to calculate the multi-kink energy levels in finite volume given its
factorizable $S$-matrix. In massive theories this can be done exactly up to
contributions due to off-shell and tunneling effects that fall off
exponentially with volume. As a first application we compare our analytical
predictions for the kink scattering theories conjectured to describe the
subleading thermal and magnetic perturbations of the tricritical Ising model
with numerical results from the truncated conformal space approach. In
particular, for the subleading magnetic perturbation our results allow us to
decide between the two different $S$-matrices proposed by Smirnov and
Zamolodchikov.
