Critical Behaviour of the Two Dimensional Step Model

TL;DR

This study investigates the critical behavior of the two-dimensional step model using finite-size scaling of Lee-Yang zeros, revealing a phase transition similar to the XY model and suggesting they share the same universality class.

Contribution

The paper provides evidence that the two-dimensional step model exhibits a phase transition and belongs to the same universality class as the XY model, using Lee-Yang zero analysis.

Findings

Identifies a phase transition from disordered to massless critical phase

Shows critical parameters match those of the XY model

Indicates both models share the same universality class

Abstract

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.