Absorbing state phase transitions with a non-accessible vacuum

TL;DR

This paper studies a universality class of reaction-diffusion systems with absorbing states where the vacuum is inaccessible, revealing that the critical behavior is governed by the pair-coagulation fixed point and confirming predictions through simulations.

Contribution

It identifies a new universality class of reaction-diffusion models with inaccessible vacuum states, showing that reversibility is not essential for this class and providing exact critical exponents.

Findings

Critical point at zero creation rate confirmed

Critical exponents are exactly computed in any dimension

Monte Carlo simulations validate theoretical predictions

Abstract

We analyze from the renormalization group perspective a universality class of reaction-diffusion systems with absorbing states. It describes models where the vacuum state is not accessible, as the set of reactions $2 A \to A$ together with creation processes of the form $A \to n A$ with $n \geq 2$. This class includes the (exactly solvable in one-dimension) {\it reversible} model $2 A \leftrightarrow A$ as a particular example, as well as many other {\it non-reversible} reactions, proving that reversibility is not the main feature of this class as previously thought. By using field theoretical techniques we show that the critical point appears at zero creation-rate (in accordance with exact results), and it is controlled by the well known pair-coagulation renormalization group fixed point, with non-trivial exactly computable critical exponents in any dimension. Finally, we report on Monte-Carlo simulations, confirming all field theoretical predictions in one and two dimensions for various reversible and non-reversible models.