Determination of the potential for fundamental- and adjoint-representation sources in SU(2) in three dimensions

Pure SU(2) lattice gauge theory in three dimensions is studied by Monte Carlo simulation with a determination of the potential between fundamental- and adjoint-representation sources as a major goal. A ${32}^3$ lattice is used and Wilson loops up to 16 by 16 are measured using a modification to the standard multihit variance reduction which improves the statistics by at least a factor of 3 at $\beta =6.0\mathrm{}$. The integrated autocorrelation times measured for the loops show a peak for loops of size $\beta$ by $\beta$. The fundamental- and adjoint-representation potentials are seen to have the same functional form to very high accuracy and their numerical values are in the ratio of their Casimir operators. The string tension is extracted and scaling is seen to within a few percent over a range of couplings which correspond to a factor of 2 change in the glueball mass. Correlated errors have been taken into account in the extraction of the potentials from the Wilson-loop values.