  We investigate the idea that the effect of the truncation applied in the TCSA
method on the spectrum coincides with the effect of a suitable changing of the
coefficients of the terms in the Hamiltonian operator. The investigation is
done in the case of the critical Ising model on a strip with an external
magnetic field on one of the boundaries. A detailed quantum field theoretical
description of this model is also given, and we propose a description as a
perturbation of the infinite coupling limit. The investigation is also carried
out for a truncation method which preserves the solvability of the model. The
results of perturbative and numerical calculations presented support the above
idea and show that the qualitative behaviour of the truncated spectrum as a
function of the coupling constant depends on the truncation method.
