This article reviews our present knowledge of universality classes in nonequilibrium systems
defined on regular lattices. The first section presents the most important critical exponents …

This review addresses recent developments in non-equilibrium statistical physics. Focusing
on phase transitions from fluctuating phases into absorbing states, the universality class of …

Universal scaling behavior is an attractive feature in statistical physics because a wide
range of models can be classified purely in terms of their collective behavior due to a …

The steady-state phase diagram of the one-dimensional reaction-diffusion model 2 A→ 3 A,
2 A→ 0 is studied through the non-Hermitian density matrix renormalization group. In the …

We study a two-dimensional ferromagnetic Ising model in which spins are updated using
modified versions of the Metropolis and Glauber algorithms. These update rules do not obey …

We study two models with n equivalent absorbing states that generalize the Domany-Kinzel
cellular automaton and the contact process. Numerical investigations show that for n= 2 both …

We analyze a two-offspring branching annihilating random walk (n= 2 BAW) model, with
finite annihilation rate. The finite annihilation rate allows for a dynamical phase transition …

The well-established universality classes of absorbing critical phenomena are directed
percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with …

We study nonequilibrium dynamical models with two absorbing states: interacting monomer-
dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models …

Numerical simulations and cluster mean-field approximations with coherent anomaly
extrapolation show that the critical line of the 1 d annihilation-fission process is separated …