Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states

Abstract

At non-equilibrium phase transitions into absorbing (trapped) states, it is well known that the directed percolation (DP) critical scaling is shared by two classes of models with a single (S) absorbing state and with infinitely many (IM) absorbing states. We study the crossover behavior in one dimension, arising from a considerable reduction of the number of absorbing states (typically from the IM-type to the S-type DP models), by following two different (excitatory or inhibitory) routes which make the auxiliary field density abruptly jump at the crossover. Along the excitatory route, the system becomes overly activated even for an infinitesimal perturbation and its crossover becomes discontinuous. Along the inhibitory route, we find continuous crossover with the universal crossover exponent $\varphi \simeq 1.78(6)$, which is argued to be equal to ${\nu }_{\Vert }$, the relaxation time exponent of the DP universality class on a general footing. This conjecture is also confirmed in the case of the directed Ising (parity-conserving) class. Finally, we discuss the effect of diffusion to the IM-type models and suggest an argument why diffusive models with some hybrid-type reactions should belong to the DP class.

8 pages, 9 figures

References in corpus (5)

• The non-equilibrium phase transition of the pair-contact process with diffusion
• Driven Pair Contact Process with Diffusion
• The phase transition of the diffusive pair contact process revisited
• Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion
• Generating function, path integral representation, and equivalence for stochastic exclusive particle systems

Cited by in corpus (4)

• Generic Absorbing Transition in Coevolution Dynamics
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Three different routes from the directed Ising to the directed percolation class
• Crossovers from parity conserving to directed percolation universality