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Asymptotically exact scaling for nonequilibrium static and dynamic critical behaviour

Monday 9th January 2006 - 14:00 to 14:50
INI Seminar Room 1

We present a scaling approach which we have recently developed for nonequilibrium static and dynamic critical behaviour. It is based on majority rule blocking implemented using complete operator algebra descriptions. These latter descriptions are generally available for particle exclusion models, but have only been pushed to an exact solution for special cases such as the steady-state of the Asymmetric Exclusion Process (biassed hopping of hard core particles). For that particular process we first show how the static scaling can be obtained using the reduced algebra which describes the steady state. We then outline how the full static and dynamic scaling follows from the complete operator algebra. The method gives for any (odd) dilatation factor $b$ the exact critical condition and exponent relations. For $b \rightarrow \infty$, it gives exact values for each exponent, including the dynamic exponent. Generalisations, eg to the partially asymmetric case, and applications, eg to relaxational dynamics of profiles and correlation functions, will be indicated.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons