Crossovers from parity conserving to directed percolation universality

Abstract

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric absorbing phases (the cellular automaton version of the nonequilibrium kinetic Ising model (NEKIMCA) and a stochastic cellular automaton invented by Grassberger, Krause, and von der Twer [J. Phys. A 17, L105 (1984)]) the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation (DP) and the crossover exponent: 1/phi approximately equal to 0.53(2) . In the case of a branching and annihilating random walk model with an even number of offspring (dual to NEKIMCA) the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the DP class characterized by the crossover exponent: 1/phi approximately equal to 0.205(5) . The two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the DP universality class in one dimension. These subclasses differ in cluster scaling exponents.

Asymmetric Mutualism in Two- and Three-Dimensional Range Expansions

“…As in typical cross-over phenomena [23], the phase boundaries near the DP2 point are given by r ∼ ±[s c (r) − s c (0)] φ , where s c (0) = 2α c ≈ 0.2484 and φ is a cross-over exponent [24]. We find φ ≈ 1.9(1) (see the Appendix), consistent with studies of related models [25]. Hence, we confirm that our model is in the same universality class as Eq.…”

Generalized contact process with two symmetric absorbing states in two dimensions

“…The behavior in the vicinity of the transition line is controlled by the dynamics of the I 1 -I 2 domain walls which is not critical for µ cp c < µ < µ * . Crossovers between various universality classes of absorbing state transitions in one dimension have been investigated by several authors [24][25][26][27]. Some of the scenarios lead to conventional crossover scaling (of the type σ c ∼ (µ − µ cp c ) 1/φ ).…”

Crossover behaviors in branching annihilating attracting walk

“…The validity of this assertion can be checked by studying what will happen if the condition is not met. Indeed, there are (at least) three different ways of breaking the condition and each way mediates distinct crossover from the DI class to the directed percolation (DP) universality class [5,9,10]. The short-range interaction is also believed to be an important premise because the long range Lévy flight changes the critical behavior [11].…”