  (2+1)-dimensional Georgi-Glashow model is explored in the regime when the
Higgs boson is not infinitely heavy, but its mass is rather of the same order
of magnitude as the mass of the W boson. In the weak-coupling limit, the Debye
mass of the dual photon and the expression for the monopole potential are
found. The cumulant expansion applied to the average over the Higgs field is
checked to be convergent for the known data on the monopole fugacity. These
results are further generalized to the SU(N)-case. In particular, it is found
that the requirement of convergence of the cumulant expansion establishes a
certain upper bound on the number of colours. This bound, expressed in terms of
the parameter of the weak-coupling approximation, allows the number of colours
to be large enough. Finally, the string tension and the coupling constant of
the so-called rigidity term of the confining string are found at arbitrary
number of colours.
