  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.
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