  We examine the Kosterlitz-Thouless universality class and show that essential
scaling at this type of phase transition is not self-consistent unless
multiplicative logarithmic corrections are included. In the case of specific
heat these logarithmic corrections are identified analytically. To identify
those corresponding to the susceptibility we set up a numerical method
involving the finite-size scaling of Lee-Yang zeroes. We also study the density
of zeroes and introduce a new concept called index scaling. We apply the method
to the XY-model and the closely related step model in two dimensions. The
critical parameters (including logarithmic corrections) of the step model are
compatable with those of the XY-model indicating that both models belong to the
same universality class. This result then raises questions over how a vortex
binding scenario can be the driving mechanism for the phase transition.
Furthermore, the logarithmic corrections identified numerically by our methods
of fitting are not in agreement with the renormalization group predictions of
Kosterlitz and Thouless.
