Polyakov loop and spin correlators on finite lattices A study beyond the mass gap

We derive an analytic expression for point-to-point correlation functions of the Polyakov loop based on the transfer matrix formalism. For the $2d$ Ising model we show that the results deduced from point-point spin correlators are coinciding with those from zero momentum correlators. We investigate the contributions from eigenvalues of the transfer matrix beyond the mass gap and discuss the limitations and possibilities of such an analysis. The finite size behaviour of the obtained $2d$ Ising model matrix elements is examined. The point-to-point correlator formula is then applied to Polyakov loop data in finite temperature $SU(2)$ gauge theory. The leading matrix element shows all expected scaling properties. Just above the critical point we find a Debye screening mass ${\mu }_D\mathrm{/}T\approx 4$, independent of the volume.