Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz

Details Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz

2007-02-22

arxiv.org/abs/cond-mat/0702524v2

Phys. Rev. E 76, 051111 (2007)

Physics

Condensed Matter

Statistical Mechanics

LaTeX, 10 pages, 10 figures. Improved version to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.76.051111

We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz that yields quantitatively accurate results for strong coupling. We obtain analytic results not only for steady state mean fields and distribution widths, but also for the dynamical approach to a steady state or to collective oscillatory behaviors in multi-field systems. Because the theory yields dynamical information, it can also predict the initial-condition-dependent final state (disordered state, steady or oscillatory ordered state) in multistable arrays.

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