  Employing a variant of the Multicanonical Ensemble we study twisted spin
configurations on periodic boxes in the $D=2$ $O(3)$ nonlinear sigma model for
$\beta$-values inbetween $1.55$ to $3.1$. The free energy difference of twisted
spin configurations is determined from the constraint effective potential. The
finite size scaling behavior is in accordance with the asymptotically free
nature of the continuum theory. Upon certain reasonable assumptions we
determine the $\Delta \beta( \beta)$-shift of the stiffness correlation length
$\xi_s$. The mass-gap as determined by our analysis is
${m_0}=79.6(1.9)~\Lambda_{latt}$. This value agrees with the analytical result
of the thermodynamic Bethe Ansatz ${m_0}=80.1~\Lambda_{latt}$.
