Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory

We consider the expectation value of a Polyakov loop in 3d SU(2) lattice Yang–Mills theory and transform it to the dual representation in terms of sums over spins. The spin dependence of the amplitudes is computed explicitly by a graphical method. We also determine the asymptotic (large spin) limit of the amplitude factors.