Multicanonical Study of Continuum Physics in the D=2 $O(3)$ Nonlinear Sigma Model

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 $\mathrm{\Delta }\beta (\beta )$-shift of the stiffness correlation length ${\xi }_s$. The mass-gap as determined by our analysis is $m_0=79.6(1.9){\mathrm{\Lambda }}_{latt}$. This value agrees with the analytical result of the thermodynamic Bethe Ansatz $m_0=80.1{\mathrm{\Lambda }}_{latt}$.