Towards Classification of Phase Transitions in Reaction--Diffusion Models

TL;DR

This paper proposes a classification scheme for phase transitions in reaction-diffusion models based on the topology of Hamiltonian phase portraits, identifying four stable classes under RG transformations.

Contribution

It introduces a novel topological classification of non-equilibrium phase transitions in reaction-diffusion systems using Hamiltonian phase portraits.

Findings

Four topologically distinct classes of phase portraits identified

Classification stable under renormalization group transformations

Applicable to models with absorbing states

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.