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 μD/T∼4, independent of the volume. (orig.)