The Kosterlitz-Thouless universality class

We examine the Kosterlitz--Thouless universality class and show that conventional (essential) scaling at this type of phase transition is self--consistent only if modified by multiplicative logarithmic corrections. 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 calls into question the vortex binding scenario as the driving mechanism for the phase transition in the XY--model. Furthermore, the logarithmic corrections identified numerically are NOT in agreement with the renormalization group predictions of Kosterlitz and Thouless