Heriot-Watt Mathematics Report Series
HWM04-4, 19 Jan 2004

The Lee-Yang Zeroes of a Traffic Jam

R Blythe, W Janke, D A Johnston and R Kenna


Abstract

The Asymmetric Exclusion Process (ASEP) one of the few exactly solved non-equilbrium models and has been a paradigm for driven diffusive systems. It has been solved for several different update dynamics including random sequential, sublattice parallel and parallel updates. The parallel update ASEP is a special case of the Nagel-Schrekenberg model for traffic flow and the transitions in the model can be interpreted as jamming transitions for the traffic in a one dimensional flow.

Recently, Blythe and Evans have considered the application of the Lee-Yang theory of partition function zeroes to the random sequential update ASEP. They found that the ASEP normalization plays the role of the partition function in equilibrium systems and that the nature of the transitions can, indeed, be derived from the behaviour of the normalization zeroes. In this paper we consider the exact solution of the parallel update ASEP and calculate the normalization zeroes both analytically and numerically. The Lee-Yang theory is found to still apply, suggesting that an equilibrium lattice path interpretation of the model exists, similar to that recently found in the random case by Brak.et.al.

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