2000-03

Phase transitions in one-dimensional nonequilibrium systems

The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is known exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We ana...

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