The application of the Yang-Lee theory to study a phase transition in a non-equilibrium system

We study a phase transition in a non-equilibrium model first introduced in ref. 5, using the Yang - Lee description of equilibrium phase transitions in terms of both canonical and grand canonical partition function zeros. The model consists of two different classes of particles hopping in opposite directions on a ring. On the complex plane of the diffusion rate we find two regions of analyticity for the canonical partition function of this model which can be identified by two different phases. The exact expressions for both distribution of the canonical partition function zeros and their density are obtained in the thermodynamic limit. The fact that the model undergoes a second-order phase transition at the critical point is confirmed. We have also obtained the grand canonical partition function zeros of our model numerically. The similarities between the phase transition in this model and the Bose-Einstein condensation has also been studied.