  We study the particle spectrum M_n(h) in the two-dimensional ferromagnetic
Ising field theory in a weak external magnetic field h. According to Wu and
McCoy scenario of the weak confinement, pairs of fermions (domain walls) are
coupled into bosonic kink-antikink bound states at small h>0. Fluctuations with
more than two fermions also contribute to the wave functions of the compound
particles, leading to the multi-fermion corrections to their masses M_n(h) in
higher orders in h. We describe a perturbative procedure, which allows to
account both multi-fermion fluctuations, and the long-range confining
interaction between fermions, and leads to the formfactor expansions for the
renormalized parameters of the model. We obtain integral representations for
the third-order multi-fermion correction to the mass M_n(h), which arise from
the regular correction to the kernel of the Bethe-Salpeter equation.
