Critical Behaviour of the Two Dimensional Step Model

We use finite–size scaling of Lee–Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn $O(2)$ model. We present evidence that, like the closely related $XY$–model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corrections) are compatible with those of the $XY$–model indicating that both models belong to the same universality class.