Universality classes in nonequilibrium lattice systems

TL;DR

This paper reviews the current understanding of universality classes in nonequilibrium lattice systems, covering static and dynamical behaviors, phase transitions, coupled systems, and their relation to interface growth models.

Contribution

It provides a comprehensive overview of known nonequilibrium universality classes, including new insights into dynamical and coupled systems, and discusses their connections to interface growth.

Findings

Identification of various nonequilibrium universality classes

Analysis of dynamical extensions and mixing effects

Mapping to interface growth models

Abstract

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.