Towards Classification of Phase Transitions in Reaction--Diffusion Models

Abstract

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the ``coordinate'' to the ``phase'' space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero ``energy''. We identify four families of topologically distinct classes of phase portraits stable upon RG transformations.

14 pages, 9 figures

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• Crossovers from parity conserving to directed percolation universality
• Aging processes in reversible reaction-diffusion systems
• Absorbing state phase transitions with a non-accessible vacuum