  I consider the dilute monopole gas expansion of the three dimensional
Yang-Mills-Higgs system in the symmetry broken phase. The functional
determinants which occur in such an expansion are computed in the heat kernel
approximation for an arbitrary $SU(N)$ gauge group. Explicit expressions for
the gauge boson mass in the unbroken gauge sector and the string tension are
obtained for the $SU(2)$ gauge model and are evaluated numerically. The results
show a strong dependence on the ratio $m_{\rm Higgs}/m_W$.
