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

TL;DR

This paper establishes an exact mapping between the FA spin model and a reaction-diffusion system, revealing the upper critical dimension as two and providing exact critical exponents across dimensions.

Contribution

It introduces a novel exact mapping between the FA model and annihilating random walks, clarifying their critical behavior and universality class.

Findings

Upper critical dimension of FA model is 2.

Critical exponents are exactly known in all dimensions.

Models do not belong to the directed percolation universality class.

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.