Critical behavior of the two-dimensional step model

We use finite-size scaling of Lee-Yang partition function zeros to study the critical behavior 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.