Mappings between reaction–diffusion and kinetically constrained systems:A+A ↔ A and the Fredrickson–Andersen model have upper critical dimensiondc = 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 thevacuum, A + A ↔ 0. We discuss the geometric structure of the mapping and its consequences for symmetriesof the models. Hence we are able to show that the upper critical dimension of the FAmodel is two, and that critical exponents are known exactly in all dimensions.These conclusions also generalize 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 themodels considered do not fall into the directed percolation universality class.