Yang-Lee Zeros for an Urn Model for the Separation of Sand
I. Bena1 , F. Coppex1 , M. Droz1 , A. Lipowski1,2
1 Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland
2 Department of Physics, A. Mickiewicz University, 61-614 Pozna´n, Poland
Phys. Rev. Lett., 91, 160602-1 – 160602-4 (2003)
We apply the Yang-Lee theory of phase transitions to an urn model for the separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity z. Numerical calculations show that in the thermodynamic limit the zeros of the effective partition function are located on the unit circle in the complex z plane. In the complex plane of the actual control parameter, certain roots converge to the transition point of the model. Thus, the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.