Universality classes in nonequilibrium lattice systems

By Géza Ódor. 2002

618 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e987ccf4f276ce2796da0c550a77d544eea31f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Mauro Mobilia
2. Ulrich Dobramysl
3. M. Pleimling
4. A. Eichhorn
5. L. Canet
6. W. Metzner
7. Uwe Claus Täuber
8. Malte Henkel

In Materials Chemistry

1. Mauro Mobilia
2. Uwe Claus Täuber
3. Malte Henkel
4. S. Lübeck
5. M. Pleimling

In Mathematical Physics

1. A. Eichhorn
2. Mauro Mobilia
3. L. Canet
4. W. Metzner
5. N. Dupuis
6. M. Tissier
7. N. Wschebor
8. Ulrich Dobramysl

Citations in the corpus

• Non-Equilibrium Phase Transitions (2010, background): “From a methodological point of view, this situation results in a large variety of universality classes without general tools for their characterisation [3].”
• The nonperturbative functional renormalization group and its applications (2020, background): “The most common ones are absorbing phase transitions, which separate an active fluctuating steady-state from one, or several, absorbing states, with no fluctuations [457–459].”
• Stochastic population dynamics in spatially extended predator–prey systems (2017, background): “On quite general grounds, one expects the critical properties of non-equilibrium phase transitions from an active phase to an absorbing state to be described by the universality class of critical directed percolation, with directionality set along the time ‘direction’ [91, 92, 93, 94, 60].”
• Geometry of quantum phase transitions (2019, background): “universality classes without general tools for their characterisation [360, 361].”
• UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS (2004, background): “Instead of going into the details we refer the interested readers to the reviews [7, 8, 90].”