The analysis of Polyakov loop and spin correlators in finite volumes

We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye screening mass $~\mu_D/T\approx4~$, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.