Mappings between reaction-diffusion and kinetically constrained systems: A+A <-> A and the FA model have upper critical dimension d_c=2

Abstract

We present an exact mapping between two simple spin models: the Fredrickson-Andersen (FA) model and a model of annihilating random walks with spontaneous creation from the vacuum, A+A <-> 0. We discuss the geometric structure of the mapping and its consequences for symmetries of the models. Hence we are able to show that the upper critical dimension of the FA model is two, and that critical exponents are known exactly in all dimensions. These conclusions also generalise to a mapping between A+A <-> 0 and the reaction-diffusion system in which the reactions are branching and coagulation, A+A <-> A. We discuss the relation of our analysis to earlier work, and explain why the models considered do not fall into the directed percolation universality class.

34 pages, 5 figures

References in corpus (12)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Glassy dynamics of kinetically constrained models
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Coarse-grained microscopic model of glass formers
• What do we learn from the shape of the dynamical susceptibility of glass-formers?
• Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids
• Field Theory of Branching and Annihilating Random Walks
• Dynamic criticality in glass-forming liquids
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• Renormalization group study of a kinetically constrained model for strong glasses
• Activated aging dynamics and negative fluctuation-dissipation ratios
• Facilitated spin models in one dimension: a real-space renormalization group study

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