Quantum Physics Division

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Yang-Lee Zeros for an Urn Model for the Separation of Sand

I. Bena^{1}
,
F. Coppex^{1}
,
M. Droz^{1}
,
A. Lipowski^{1,2}

^{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)**

**DOI:** 10.1103/PhysRevLett.91.160602

Abstract:

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.

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