  In the ferromagnetic phase of the q-state Potts model, switching on an
external magnetic field induces confinement of the domain wall excitations. For
the Ising model (q = 2) the spectrum consists of kink-antikink states which are
the analogues of mesonic states in QCD, while for q = 3, depending on the sign
of the field, the spectrum may also contain three-kink bound states which are
the analogues of the baryons. In recent years the resulting "hadron" spectrum
was described using several different approaches, such as quantum mechanics in
the confining linear potential, WKB methods and also the Bethe-Salpeter
equation. Here we compare the available predictions to numerical results from
renormalization group improved truncated conformal space approach (RG-TCSA).
While mesonic states in the Ising model have already been considered in a
different truncated Hamiltonian approach, this is the first time that a
precision numerical study is performed for the 3-state Potts model. We find
that the semiclassical approach provides a very accurate description for the
mesonic spectrum in all the parameter regime for weak magnetic field, while the
low-energy expansion from the Bethe-Salpeter equation is only valid for very
weak fields where it gives a slight improvement over the semiclassical results.
In addition, we confirm the validity of the recent predictions for the baryon
spectrum obtained from solving the quantum mechanical three-body problem.
