Dynamic phase transitions in diffusion-limited reactions

TL;DR

This paper reviews the critical behavior of non-equilibrium systems undergoing phase transitions from active to absorbing states, highlighting universality classes, critical exponents, and the effects of conservation laws and local processes.

Contribution

It provides a comprehensive review of the universality classes and critical exponents in diffusion-limited reactions, including effects of conservation laws and local processes.

Findings

Directed percolation universality class with critical dimension d_c=4.

Parity conservation leads to different critical exponents below d_c'=4/3.

The pair contact process with diffusion is a key non-trivial universality class.

Abstract

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d_c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d_c' = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues.