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